Stanislaw Ewert-Krzemieniewski (Szczecin)

**Abstract**

The MathTensor software enables to calculate the curvature invariants
of

dierentiable 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.