A Generalization of Inoue Surfaces $S^+$

TL;DR

This paper constructs new high-dimensional compact complex manifolds with flat affine structures using Lie groups, generalizing the Inoue surfaces $S^+$ in two dimensions, and broadening the understanding of such geometric structures.

Contribution

It introduces a method to generate higher-dimensional examples of compact complex manifolds with flat affine structures, extending the known Inoue surfaces $S^+$ to arbitrary dimensions.

Findings

New examples of compact complex manifolds with flat affine structures in high dimensions

Retrieval of Inoue surfaces $S^+$ as a special case in two dimensions

Framework for constructing complex manifolds with specific geometric properties

Abstract

Using Lie groups with left-invariant complex structure, we construct new examples of compact complex manifolds with flat affine structure in arbitrarly high dimensions. In the 2-dimensional case, we retrieve the Inoue surfaces $S^+$.