Computing of Curvature Invariants in Arbitrary DimensionStanislaw Ewert-Krzemieniewski
Technical University of Szczecin
The MathTensor software enables one to calculate the curvature invariants of differentiable manifolds in the case that the dimension of manifold under consideration is a concrete number. When proving the existence of geometric objects it is important to have examples for all dimensions n, greater or equal to some , that is, when the dimension is just a symbol. The aim of this 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.
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