Compact K\"ahler contact manifolds

TL;DR

This paper proves that non-projective compact Kähler contact manifolds are essentially projectivized tangent bundles of compact Kähler manifolds, providing a classification result in complex geometry.

Contribution

It establishes a classification of non-projective compact Kähler contact manifolds as projectivizations of tangent bundles.

Findings

Non-projective compact Kähler contact manifolds are of the form P T_Y.

Provides a classification linking contact manifolds to tangent bundle projectivizations.

Advances understanding of the structure of Kähler contact manifolds.

Abstract

We prove that a non-projective compact K\"ahler contact manifold is of the form $\mathbb{P} T_Y$, where $Y$ is a compact K\"ahler manifold.