# On rigidity of locally symmetric spaces

## TL;DR

This paper extends classical rigidity results to certain non-compact locally symmetric spaces, specifically those formed by quotients of hermitian symmetric domains by arithmetic groups, broadening understanding of their geometric properties.

## Contribution

It generalizes Calabi-Vesentini's rigidity theorems to non-compact locally symmetric spaces arising from arithmetic quotients.

## Key findings

- Rigidity results hold for a broader class of non-compact locally symmetric spaces.
- The work applies to quotients of hermitian symmetric domains by neat arithmetic subgroups.
- It provides new insights into the geometric structure of these spaces.

## Abstract

In this note I generalize the classical results of Calabi-Vesentini to certain non-compact locally symmetric domains, namely those that are quotients of a hermitian symmetric domain by a neat arithmetic subgroup of the group of its holomorphic automorphisms.