Index of quasi-conformally symmetric semi-Riemannian manifolds

TL;DR

This paper determines the index of semi-Riemannian manifolds that exhibit quasi-conformal and concircular symmetry with respect to a metric connection, advancing understanding of their geometric structure.

Contribution

It introduces the calculation of the index for manifolds with specific symmetries related to a metric connection, a novel contribution in differential geometry.

Findings

Computed the index for $ ilde{ abla}$-quasi-conformally symmetric manifolds.

Determined the index for $ ilde{ abla}$-concircularly symmetric manifolds.

Extended the classification of semi-Riemannian manifolds based on symmetry properties.

Abstract

We find the index of $\widetilde{\nabla}$-quasi-conformally symmetric and $\widetilde{\nabla}$-concircularly symmetric semi-Riemannian manifolds, where $\widetilde{\nabla}$ is metric connection.