Splitting submanifolds of families of fake elliptic curves

TL;DR

This paper classifies splitting submanifolds within families of fake elliptic curves, completing the understanding of such structures in threefolds with projective structures.

Contribution

It provides a complete classification of splitting submanifolds in these specific geometric contexts, extending previous results to new cases.

Findings

Classification of all splitting submanifolds in families of fake elliptic curves

Completes the case for threefolds with a projective structure

Shows that splitting submanifolds are totally geodesic in certain conditions

Abstract

Let N a compact complex submanifold of a compact complex manifold M. We say N splits in M, if the holomorphic tangent bundle sequence splits holomorphically. By a result of Mok a splitting submanifold of a Kaehler Einstein manifold with a projective structure is totally geodesic. The classification of all splitting submanifolds of families of fake elliptic curves given here completes the case of threefolds M with a projective structure by a previous result of the authors.