Uniformizations of compact Sasakian manifolds

TL;DR

This paper establishes a criterion for deforming compact Sasakian manifolds into locally isomorphic circle bundles over Hermitian symmetric spaces, extending Simpson's uniformization results to the Sasakian setting.

Contribution

It introduces a new deformation criterion for compact Sasakian manifolds, linking them to symmetric space structures as a Sasakian analogue of Simpson's uniformization theory.

Findings

Deformation criterion for compact Sasakian manifolds.

Connection to circle bundles over Hermitian symmetric spaces.

Extension of Simpson's uniformization results.

Abstract

We give a criterion for compact Sasakian manifolds to be deformed to Sasakian manifolds which are locally isomorphic to circle bundles of anti-canonical bundles over Hermitian symmetric spaces as a Sasakian analogue of Simpson's uniformization results related to variations of Hodge structure and Higgs bundles.