Rigidity of Oeljeklaus-Toma manifolds

TL;DR

This paper proves that Oeljeklaus-Toma manifolds of simple type are rigid and that all line bundles on them are flat, revealing their geometric and topological properties.

Contribution

It establishes the rigidity of simple type Oeljeklaus-Toma manifolds and characterizes their line bundles as flat, advancing understanding of their complex structure.

Findings

Oeljeklaus-Toma manifolds of simple type are rigid

All line bundles on these manifolds are flat

Provides new insights into their geometric structure

Abstract

We prove that Oeljeklaus-Toma manifolds of simple type are rigid, and that any line bundle on an Oeljeklaus-Toma manifold is flat.