Computing of Curvature Invariants in Arbitrary Dimension

Stanislaw Ewert-Krzemieniewski (Szczecin)

Abstract
The MathTensor software enables to calculate the curvature invariants of
di erentiable manifolds in the case when the dimension of manifold under
consideration is a concrete number. Proving the existence of geometric ob-
jects it is important to have examples for all dimensions n; greater or equal
to some n 0 ; 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.