# 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.

## Key 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.