Curvature and Weyl collineations of spacetimes

TL;DR

This paper investigates the symmetries of the Riemann and Weyl tensors in general relativity, exploring their interrelations and providing illustrative examples to deepen understanding of spacetime curvature structures.

Contribution

It analyzes the interrelations between curvature and Weyl collineations, offering new insights into their symmetry properties in various spacetimes.

Findings

Identified specific conditions for symmetries of Riemann and Weyl tensors.

Provided examples illustrating the interrelations of these symmetries.

Enhanced understanding of curvature structure in general relativity.

Abstract

Lie symmetries of various geometrical and physical quantities in general relativity play an important role in understanding the curvature structure of manifolds. The Riemann curvature and Weyl tensors are two fourth-rank tensors in the theory. Interrelations between the symmetries of these two tensors (known as collineations) are studied. Some illustrative examples are also provided.