# On compact splitting complex submanifolds of quotients of bounded symmetric domains

## TL;DR

This paper investigates the properties of compact complex submanifolds within quotients of bounded symmetric domains, focusing on characterizing those that are totally geodesic among splitting submanifolds.

## Contribution

It provides a characterization of totally geodesic submanifolds among compact splitting complex submanifolds in quotients of bounded symmetric domains.

## Key findings

- Characterization of totally geodesic submanifolds
- Conditions for splitting tangent sequences
- Insights into the geometry of quotient manifolds

## Abstract

In the current article our primary objects of study are compact complex submanifolds of quotient manifolds of irreducible bounded symmetric domains by torsion free discrete lattices of automorphisms. We are interested in the characterization of the totally geodesic submanifolds among compact splitting complex submanifolds, i.e. under the assumption that the tangent sequence splits holomorphically over the submanifold.