The local structure of conformally symmetric manifolds

TL;DR

This paper advances the local classification of pseudo-Riemannian manifolds with parallel Weyl tensor, focusing on those that are neither conformally flat nor locally symmetric, completing a key step in understanding their structure.

Contribution

It provides a comprehensive local classification of conformally symmetric manifolds that are not conformally flat or locally symmetric.

Findings

Classification of such manifolds completed

Identification of key geometric properties

Extension of previous classification results

Abstract

This is a final step in a local classification of pseudo-Riemannian manifolds with parallel Weyl tensor that are not conformally flat or locally symmetric.