Uniformizations of compact Sasakian manifolds

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.

v2: Section 3.2 and proof of Theorem 4.1 are corrected. v3: Final version. To appear in IMRN. 10 pages. Comments are welcome

References in corpus (3)

• A foliated Hitchin-Kobayashi correspondence
• Energy properness and Sasakian-Einstein metrics
• Locally Homogeneous Aspherical Sasaki Manifolds