Wolfram Library Archive

Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings

Computing of Curvature Invariants in Arbitrary Dimension

Stanislaw Ewert-Krzemieniewski

1999 International Mathematica Symposium

The MathTensor software enables to calculate the curvature invariants of differentiable manifolds in the case when the dimension of manifold under consideration is a concrete number. Proving the existence of geometric objects it is important to have examples for all dimensions n; greater or equal to some n0 ; i.e. when the dimension is just a symbol. The aim of the paper is to show how, using MathTensor and Mathematica commands, one can define the covariant and contravariant components of the metric tensor. Then we will show how to define different curvature tensors and how to execute the calculation of their components.

*Mathematics > Calculus and Analysis > Differential Geometry
*Wolfram Technology > Application Packages > Applications from Independent Developers > MathTensor

MathTensor, curvature invariants, differentiable manifold, covariant components of the metric tensor, contravariant components of the metric tensor, curvature tensors