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#11. Algebraic Computations of Riemann, Ricci, Weyl Tensor

This notebook is based on the article entitled, "Algebraic Computations in General Relativity using Mathematica" published in 2007.

#12. Lanczos Potential for Weyl Metric - Sardar Patel University

It is known that the Weyl curvature tensor hijk ... tensors in the NP field equations, Lanczos ... are carried out using Mathematica programs.

#13. First heavenly partial differential equation: Mathematica file

This Mathematica file computes the Weyl tensor, the self-dual and anti-self dual parts of the Weyl tensor for the principal symbol of the ...

#14. JHEP06(2022)104 - Inspire HEP

Weyl covariance and the energy momentum tensors of ... heavily the Mathematica packages xAct [19, 20] and xTras [21] and runs in a ...

#15. The first two figures on the left give the Mathematica print of...

Our main result establishes a simple correspondence between the anti-self-dual Weyl tensor of a pKE metric with non-zero scalar curvature and the Cartan quartic ...

#16. Vanishing Results for the Cotton Tensor on ... - Springer Link

In this paper we study on gradient quasi-Einstein solitons with a fourth-order vanishing condition on the Weyl tensor.

#17. xTras - A field theory inspired xAct package for Mathematica

Generating lists of dimensional dependent identities (e.g. the vanishing of the Weyl tensor in D=3). Making any tensorial expression traceless. Symmetrizing ...

#18. On Algebraic Computations of Electric and Magnetic Parts of ...

Weyl tensor which represents pure gravitational field in general ... [6] have used Mathematica to carry out algebraic computation of spin coefficients in ...

#19. Applications of NP Formalism and GHP Formalism in General ...

2 Algebraic Computations in General Relativity using Mathematica . . 18 ... 3 Electric and Magnetic parts of the Weyl Tensor and Spin Coefficients . . 46.

#20. Notes on the Newman-Penrose formalism - Justin L. Ripley

I refer to a Mathematica note several times, which can be accessed at: ... 1.3.3 Definitions: components of Weyl and Ricci tensors .

#21. CARTAN: A Mathematica package for tensor computations

... tensor component package based on the popular Mathematica program. ... functions for computation of tensors such as Riemann, Ricci, Einstein, Weyl, ...

#22. On the kÄhler-ricci solitons with vanishing bochner-weyl tensor

Acta Mathematica Scientia · Volume 32, Issue 3, May 2012, Pages 1239-1244 ... On the kÄhler-ricci solitons with vanishing bochner-weyl tensor.

#23. The Evolution of the Weyl Tensor under the Ricci Flow

Nous calculons l'équation d'évolution du tenseur de Weyl d'une variété riemannienne par le flot de Ricci et nous discutons des conséquences pour la ...

#24. Computer Algebra Tools for Numerical Relativity - MPG.PuRe

MathTensor is a Mathematica package for tensor analysis which for our purpose ... equation that relates the Riemann tensor to the Weyl tensor, ...

#25. Models of mechanical systems preserving the Weyl tensor

The Weyl projective curvature tensor is a tensor object that ... Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis 31(1), 61–69.

#26. VATURE TENSOR OF AN N(k)-CON- TACT METRIC MANIFOLD

Mathematica Pannonica. 21/1 (2010), 129–142. ON THE WEYL PROJECTIVE CUR- ... and P(ξ, X) · Z = 0 where P is the Weyl projective curvature tensor and Z is.

#27. Vanishing Results for the Cotton Tensor on Gradient Quasi ...

... solitons with a fourth-order vanishing condition on the Weyl tensor. ... Acta Mathematica Sinica, English Series ( IF 0.833 ) Pub Date ...

#28. on a class of ricci-recurrent manifolds - Emis.de

Acta Mathematica Academiae Paedagogicae Nyıregyháziensis. 19 (2003), 71–82 ... posed on the Weyl conformal curvature tensor are investigated. The main the-.

#29. Ricci - A Mathematica package for doing tensor calculations in ...

To use Ricci and this manual, you should be familiar with Mathematica, and with the basic objects of differential geometry (manifolds, vector bundles, tensors,.

#30. Nanta mathematica, v. 3, no. 1 (July 1968-June 1969) - BookSG

This issue of Nanta mathematica contains articles on Einstein's tensor and Weyl's projective curvature tensor in conformal space, some results on ...

#31. CARTAN - CERN Document Server

Tensors such as Riemann, Ricci, Einstein, and Weyl are prede ned. It is ... In order to install Cartan 1.01 for Unix you need Mathematica and a Unix.

#32. The Geometry of Weakly Self-dual Kähler Surfaces

We study Kähler surfaces with harmonic anti-self-dual Weyl tensor. We provide an explicit local description, which we use to obtain the complete ...

#33. Cyclic Cosmologies - Técnico Lisboa - Autenticação

It is important to note that in our Mathematica code the Riemann tensor Rµνρσ, which there is defined as riemann, is not defined through the Weyl tensor as ...

#34. Vanishing Results for the Cotton Tensor on Gradient Quasi ...

Key words. Gradient quasi-Einstein soliton / Cotton tensor / Weyl tensor / locally conformally flat ... Acta Mathematica Sinica.

#35. On a Type of P-Sasakian Manifolds Uday Chand De, Cihan ...

Key Words: para-Sasakian manifold, projective curvature tensor, Weyl tensor, Ricci tensor, Einstein manifold and η-Einstein manifold. 1. Introduction.

#36. Note (a) for The Phenomenon of Gravity - Wolfram Science

(In Mathematica, the explicit form of such a tensor can be represented as a ... by the Ricci tensor correspond to the so-called Weyl tensor; for d = 2.

#37. [PDF] CARTAN: A Mathematica package for tensor computations

CARTAN has predefined functions for computation of tensors such as Riemann, Ricci, Einstein, Weyl, as well as other tensors and invariants.

#38. Computer Algebra Tools for Numerical Relativity - CiteSeerX

MathTensor is a Mathematica package for tensor analysis which for our purpose ... equation that relates the Riemann tensor to the Weyl tensor, ...

#39. Introducing new system: Redberry

Figure 2: Comparison of Redberry performance with Mathematica xAct, ... Tensor computer algebra in theoretical physics ... //Weyl tensor symmetries.

#40. Acta Universitatis Palackianae Olomucensis. Facultas Rerum ...

Mathematica. Filip Defever; Ryszard Deszcz. On Riemannian manifolds satisfying a certain curvature condition imposed on the. Weyl curvature tensor.

#41. The Weyl Curvature Tensor of Hypersurfaces Under the Mean ...

In this paper, we study the evolution of the Weyl curvature tensorWof hypersurfaces inRn+1under the mean curvature flow. We find a bound forthe Weyl ...

#42. Acta Mathematica Sinica, English Series

Acta Mathematica Sinica, English Series. Feb., 2013, Vol. ... Generalized Einstein Tensor for a Weyl Manifold and Its Applications. Abdülkadir ¨OZDE˘GER.

#43. How do we find the Ricci tensor in Maple or in other ... - Quora

... a contraction of the Riemann tensor) , the Weyl tensor, and the Einstein tensor. ... What are some free alternatives to Maple or Mathematica for doing ...

#44. Complete Riemannian manifolds admitting a pair of Einstein ...

Ghosh, Amalendu. "Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures." Mathematica Bohemica 141.3 (2016): 315-325. <http://eudml.org/doc ...

#45. Perturbative analysis of the Conformal Constraint Equations in ...

Mathematica —information and documentation on the xAct suite can be found on ... in the Weyl tensor, which in (1, 3) form is conformally covariant:.

#46. software for a conformally invariant yang-Mills type energy ...

These notebooks contain Ricci and Mathematica software commands ... to the Shouten and Weyl tensors and the tractor curvature.

#47. On some curvature conditions of pseudosymmetry type

Manifolds with parallel Weyl tensor having Ricci tensor of rank two form a ... Therefore we also investigate Roter type manifolds for which the tensors $$R ...

#48. ON THE K¨AHLER-RICCI SOLITONS WITH VANISHING ...

Acta Mathematica Scientia 2012,32B(3):1239–1244 http://actams.wipm.ac.cn ... Key words Ricci flow; Kahler Ricci soliton; Bochner-Weyl tensor.

#49. ‪Ravi Panchal‬ - ‪Google 學術搜尋‬

Algebraic computations of general observer quantities using Mathematica ... Electric and magnetic parts of the Weyl tensor and spin coefficients.

#50. MATHEMATICA BOHEMICA, Vol. 126, No. 3, pp. 631-637, 2001

We apply this result to Weyl curvature tensors. Keywords: traceless tensor, trace decomposition, almost projective invariant.

#51. Almost Kähler 4-manifolds with J-invariant ricci tensor and ...

Almost Kähler 4-manifolds with J-invariant ricci tensor and special weyl tensor. Vestislav Apostolov,. Vestislav Apostolov.

#52. CalculateChristoffels

Calculate the Weyl tensor. In[15]:= weyldown = CalculateWeyldown@metric, riemannd, ricci, Rscalar, simplifyroutineD;. 2. Printed from the Mathematica Help ...

#53. Is there software I can use for tensor calculations?

... doing symbolic calculations of tensors (Riemann-Einstein-Ricci etc.) ... but these are usually based on the Mathematica program, which I ...

#54. Best Symbolic Language - Physics Forums

Mathematica seems to the most popular, but seems to contain a few quirks, ... Ricci Tensor, Ricci scalar, Einstein Tensor, Weyl Tensor, ...

#55. Al-Zamil ON WEYL TENSOR OF ACR-MANIFOLDS OF ...

In this paper, we determine the components of the Weyl tensor of almost ... Y.J. On weakly semiconformally symmetric manifolds, Acta Mathematica Hungarica,.

#56. Beyond the Black Hole Horizon with Mathematica - YouTube

To learn more about Wolfram Technology Conference, please visit:https://www.wolfram.com/events/technology-conference/Speaker: Max ...

#57. Vanishing Results for the Cotton Tensor on Gradient Quasi ...

Acta Mathematica Sinica, English Series ... Keywords Gradient quasi-Einstein soliton, Cotton tensor, Weyl tensor, locally conformally flat.

#58. SimpleTensor – a user-friendly Mathematica package for ...

We present OGRe, a modern Mathematica package for tensor calculus, ... examine applications of SimpleTensor to Dirac and Weyl particles.

#59. Linear perturbations of special spacetimes

Symmetric trace-free tensors. Symmetric spinors. Ricci scalar R. 24Λ. Trace-free Ricci Sab. −2ΦABA B. Weyl tensor Cabcd.

#60. Riemannian Geometry

Printed from: Wolfram Mathematica - Complete Documentation 1. ©1988–2008 Wolfram Research, ... The Weyl tensor, W, is defined by the formula in coordinates:.

#61. capabilities of the mathematica package 'riemannian ...

CAPABILITIES OF THE MATHEMATICA PACKAGERIEMANNIAN GEOMETRY AND TENSOR CALCULUS ... of thesecond tensor, giving the square of the Weyl tensor W abmnWmncd.

#62. Characterizations of twisted product manifolds to be warped ...

... on the Weyl conformal curvature tensor and the Weyl projective tensor. ... Acta Mathematica Universitatis Comenianae, 82(2), 253-263.

#63. physics - Mathematica packages written in Wolfram Language

OGRe is a modern Mathematica package for tensor calculus, designed to be both powerful and user-friendly. It can be used in a variety of contexts where ...

#64. ‪A.H. Hasmani‬ - ‪Google Scholar‬

Algebraic computations of general observer quantities using Mathematica ... Newman-Penrose formalism and electric and magnetic parts of Weyl tensor.

#65. Critical Metrics for the L2-norm of the Curvature Tensor

should mention at least one other functional, the L2-norm of the Weyl tensor, which has been studied by both mathematicians and physicists. In chapter one.

#66. xPand. Documentation - page index

xAct`xPand` is a Mathematica Package which provides tools to compute formally the cosmological ... DefTensor: Defining Weyl tensor WeylCDah2.

#67. The Weyl tensor correlator in cosmological spacetimes

We give a general expression for the Weyl tensor two-point function in a general ... 2014 xAct: efficient tensor computer algebra for Mathematica, ...

#68. Acta Mathematica Sinica, English Series

Cover Image Acta Mathematica Sinica, English Series ... on gradient quasi-Einstein solitons with a fourth-order vanishing condition on the Weyl tensor.

#69. Weyl tensor - Encyclopedia of Mathematics

In Riemannian geometry one has a manifold M of dimension n which admits a metric tensor g whose signature is arbitrary.

#70. ON WEYL TENSOR OF ACR-MANIFOLDS OF CLASS C12 ...

In this paper, we determine the components of the Weyl tensor of almost contact ... Suh Y.J. On weakly semiconformally symmetric manifolds, Acta Mathematica ...

#71. On printing expressions using TexAct - Google Groups

to xAct Tensor Computer Algebra ... (Ricci scalar/tensor and Riemann/Weyl tensor) in the standard format, ... Mathematica 11.0 for Linux in my case).

#72. Phys 514 - Assignment 6 Solutions - McGill Physics

b) Calculate the Riemann tensor, Ricci tensor, and Ricci scalar. ... d) Since the Weyl tensor is 0, let us rewrite the Riemann tensor in ...

#73. curvature properties of some four-dimensional manifolds

DEMONSTRATE MATHEMATICA. Vol. XXXTV ... where C is the (Weyl) conformal curvature tensor of g and the tensor S • C is defined by.

#74. Source for Principal Null Directions Kerr, Example Worksheet

In the Worksheet "Walker-Penrose Killing tensor in Kerr spacetime" ... I have difficulties verifying (with Mathematica) that this is indeed ...

#75. On Almost C(a)-Manifold Satisfying Some Conditions On The ...

... Satisfying Some Conditions On The Weyl Projective Curvature Tensor ... curvature tensor of a Kenmotsu manifold, Mathematica Pannonica, ...

#76. Présentation Générale

Tensorial is a general purpose tensor calculus package for Mathematica 5.0 or ... Christoffel, Riemann, Ricci, Einstein, Weyl and scalar curvature routines.

#77. Some Properties of ET-Projective Tensors Obtained from Weyl ...

S. Mincic and M. Stankovic tried to generalize Weyl projective tensor in non-symmetric ... Mathematica Societatis János Bolayai, 31, Differential Geometry, ...

#78. On equivalence of differential equations - Journals

Acta et Commentationes Universitatis Tartuensis de Mathematica ... metasymplectic transformations, Weyl tensor in Spencer cohomology group, ...

#79. Electric and magnetic parts of the Weyl tensor and spin ...

It is known that electric and magnetic parts of the Weyl tensor in General Relativity ... of Spin Coefficients in Newman-Penrose Formalism using Mathematica.

#80. On Riemann and Weyl Compatible Tensors

Weyl conformal curvature tensor of an n-dimensional semi-Riemannian manifold ... M. Prvanović, On a class of SP-Sasakian manifolds, Note di Mathematica 10 ...

#81. Contributions to polynomial conformal tensors - Numdam

Key words : pseudo-Riemannian manifold, conformally invariant tensor, conformal ... to replace the Weyl tensor by the conformal tensor.

#82. Article - On some curvature conditions of pseudosymmetry type

Manifolds with parallel Weyl tensor having Ricci tensor of rank two form a ... Periodica Mathematica Hungarica , Volume 70, pp 153-170; ...

#83. Curvature Invariants for Charged and Rotating Black Holes

Riemann or curvature invariants, formed from the Riemann tensor and ... We also need the dual of the Weyl tensor, defined by [28].

#84. 由action和metric ansatz计算EOM流程示例(Mathematica) - 知乎

Mathematica 初始程序：（在运行具体计算程序前运行这两个大块就行） ... stPrint["Conformally Flat"]]], stPrint["Weyl tensor not computed", ...

#85. How to calculate scalar curvature Ricci tensor and Christoffel ...

... unlike traditionally $0,1,2,3$ for representing tensors in Mathematica by ... could define another interesting geometrical objects e.g. the Weyl tensor ...

#86. Weyl tensor

In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, ...

#87. GeneralRelativityTensors - Black Hole Perturbation Toolkit

A Mathematica package that provides a set of functions for performing coordinate-based tensor calculations with a focus on general relativity and black ...

#88. 9 5 Form G Congruence Transformations

Scripta Mathematica - 1973. Includes section "Book reviews." ... Deformation of Weyl Algebra.- ... the methods of tensor calculus and.

#89. Weyl tensor - Wikipedia

In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, ...

#90. Maple and Mathematica: A Problem Solving Approach for ...

Maple: tensorsGR, computing General Relativity curvature tensors in a coordinate ... the covariant Einstein tensor, Einstein, the covariant Weyl tensor, ...

#91. Notes on the Weyl, E/B, and 3+1 decompositions of Riemann ...

Weyl decomposition. The most basic ingredient here is splitting the Riemann tensor into trace and tracefree pieces. This should be covered ...

#92. Conventions, Definitions, Identities, and Formulas

Curvature Tensors; Differential Forms; Euler Densities ... Bianchi Identities for the Weyl Tensor ∇νCλμσν=(d−2)(∇μSλσ−∇λSμσ).

#93. Introduction to General Relativity: A Course for ...

288 Appendix E: Mathematica Packages for Tensor Calculus To launch the code ... in 0.002247 sec Ricci computed in 0.000167 sec Weyl computed in 0.000015 sec ...

#94. General Relativity and Gravitation 1992, Proceedings of the ...

... ( ii ) determination of the Petrov type of the Weyl tensor and the Segré type of ... Tensor [ 11 ] is a Mathematica - based [ 12 ] system with over 250 ...