On the structure of Hermitian manifolds with semipositive Griffiths curvature
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Abstract:
In this paper we establish partial structure results on the geometry of compact Hermitian manifolds of semipositive Griffiths curvature. We show that after appropriate arbitrary small deformation of the initial metric, the null spaces of the Chern–Ricci two-form generate a holomorphic, integrable distribution. This distribution induces an isometric, holomorphic, almost free action of a complex Lie group on the universal cover of the manifold. Our proof combines the strong maximum principle for the Hermitian Curvature Flow (HCF), new results on the interplay of the HCF and the torsion-twisted connection, and observations on the geometry of the torsion-twisted connection on a general Hermitian manifold.References
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Additional Information
- Yury Ustinovskiy
- Affiliation: Courant Institute of Mathematical Sicences, New York University, 251 Mercer Street, New York, New York, 10012
- MR Author ID: 887998
- Email: yu3@nyu.edu
- Received by editor(s): June 23, 2019
- Published electronically: May 28, 2020
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 5333-5350
- MSC (2010): Primary 53C44; Secondary 53C55
- DOI: https://doi.org/10.1090/tran/8101
- MathSciNet review: 4127878