# Linear Independence of Covariant Derivatives and Space-Curvatures

## TL;DR

This paper investigates the linear independence of curvature tensors and pseudotensors in non-symmetric affine connection spaces, exploring how many derivatives and tensors are needed for comprehensive research and potential applications in physics.

## Contribution

It determines the minimal number of covariant derivatives and tensors required for complete analysis in non-symmetric affine connection spaces and explores their linear relationships.

## Key findings

- Number of covariant derivatives needed for research clarified
- Linearly independent curvature tensors and pseudotensors identified
- Potential applications in physics discussed

## Abstract

It is developed the considerations from (S. M. Min\v{c}i\'c, [14, 15]) about curvature tensors and pseudotensors for a non-symmetric affine connection space in this paper. How many kinds of covariant derivatives are enough to be defined for complete researching in the field of non-symmetric affine connection spaces is examined here. This result is interpreted. After that, we searched how many curvature tensors and pseudotensors of a non-symmetric affine connection space are linearly independent. In the next, it is examined is it possible to express all curvature tensors as the linear combinations of the pseudotensors. At the end of this paper, we considered these results for possible applications in physics.