Complex Manifolds With Negative Curvature Operator-Reference-Cited by-同舟云学术

Complex Manifolds With Negative Curvature Operator

Published:2019-12-27 Issue:24 Volume:2021 Page:18520-18528
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Lee Man-Chun¹,Streets Jeffrey²

Affiliation:

1. Department of Mathematics, Northwestern University, Evanston, IL 60208, USA

2. Department of Mathematics, Rowland Hall, University of California Irvine, CA 92617, USA

Abstract

Abstract We prove that compact complex manifolds admitting metrics with negative Chern curvature operator either admit a $d d^c$-exact positive $(1,1)$ current or are Kähler with ample canonical bundle. In the case of complex surfaces we obtain a complete classification. The proofs rely on a global existence and convergence result for the pluriclosed flow.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2021/24/18520/41940351/rnz331.pdf

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