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Riemannian Geometry and Tensor Analysis
Author

Rolf Sulanke
Organization: Humboldt-University Berlin
Department: Mathematics
URL: http://www-irm.mathematik.hu-berlin.de/~sulanke
Revision date

2017-08-28
Description

The notebook "Pseudo-Riemannian Geometry and Tensor-Anaslysis" can be used as an interactive textbook introducing into this part of differential geometry. It continues the item "An Interactive Textbook on Euclidean Differential Geometry", MathSource 9115, but it may be used indepedently of the mentioned textbook as a starting point for applications of Mathematica in Riemannian Geometry or Relativity Theory. The file RGv2.pdf gives a survey over the contents of the notebook, and RG.zip contains the notebook and the packages with the newly introduced Mathematica functions.
Subject

*Mathematics > Calculus and Analysis > Differential Geometry
Keywords

absolute differential, absolute parallel, affine connection, algebra Lie, algebra of functions, alternated absolute, differential, antisymmetric tensors, arc length, atlas, auto-parallel curves, Bianchi's identity, bivector, category, chart, Christoffel symbols, class Ck, commutator, complete, atlas, commutator, conformal, connection forms, contraction, contravariant, coordinate transformation, covariant curvature, tensor, covector fields, curvature tensor, curve, diffeomorphism, differential, differential form, dimension, directional derivative, duality, equi, equivalent tensors, Euclidean metric, exterior algebra, exterior differential, exterior product, fiber, fiber type, flat linear connection, Gamma-symbols, Gaussian curvature, Gradient, gradient tensor, Hausdorff space, homeomorphism, hyperbolic, space, hyperboloid, hypersurface, immersiom, index, index, lowering, index raising, inner geometry, inverse metric, isotropic, Jacobi, Jacobian, Kronecker symbol, Levi-Civita connection, linear connection, local coordinates, Lorentzian space, manifolds, metric, metric tensor, multi indices, nabla, n-sphere, orientable, manifold, orientation, oriented atlas, parallel displacement, p-form, product rule, pseudo-Euclidean space, pseudo-Riemannian space, regular, Ricci tensor, Riemannian, space, Riemannian spaces of constant curvature, sectional, curvature, singular, smooth, spacelike, sphere, sphere of, imaginary radius, stereographic projection, strict coordinates, submanifold, sum convention, surface, symmetric tensors, tangent basis, tangent bundle, tangent space, tangent, vector, tensor fields, tensor metric, tensor product, timelike, torsion tensor, traditional notation, vector, fields, wedge, wedge product
Downloads

Download
RGv2.pdf (2.5 MB) - PDF Document
Download
RG.zip (924.4 KB) - ZIP archive