Curves on Endo-Pajitnov Manifolds

TL;DR

This paper investigates the existence of complex submanifolds within Endo-Pajitnov manifolds, identifying conditions for the presence or absence of compact complex curves, thus advancing understanding of their geometric structure.

Contribution

It introduces a classification of Endo-Pajitnov manifolds based on their complex submanifold content and provides algebraic criteria for the non-existence of compact complex curves.

Findings

Certain Endo-Pajitnov manifolds contain compact complex submanifolds.

An algebraic condition determines when these manifolds lack compact complex curves.

The study extends the understanding of higher-dimensional generalizations of Inoue surfaces.

Abstract

Endo-Pajitnov manifolds are generalizations to higher dimensions of the Inoue surfaces $S^M$. We study the existence of complex submanifolds in Endo-Pajitnov manifolds. We identify a class of these manifolds that do contain compact complex submanifolds and establish an algebraic condition under which an Endo-Pajitnov manifold contains no compact complex curves.