Weyl-Einstein structures on K-contact manifolds

TL;DR

This paper proves that a compact K-contact manifold admits a compatible closed Weyl-Einstein connection if and only if it is Sasaki-Einstein, establishing a precise geometric characterization.

Contribution

It provides a characterization of Sasaki-Einstein manifolds via the existence of a compatible closed Weyl-Einstein connection.

Findings

A compact K-contact manifold has a closed Weyl-Einstein connection if and only if it is Sasaki-Einstein.

The result links Weyl geometry with Sasaki-Einstein structures.

This characterization helps identify Sasaki-Einstein manifolds through Weyl connections.

Abstract

We show that a compact K-contact manifold $(M,g,\xi)$ has a closed Weyl-Einstein connection compatible with the conformal structure $[g]$ if and only if it is Sasaki-Einstein.