Vol. 288, No. 2, 2017

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ISSN: 0030-8730
On bisectional nonpositively curved compact Kähler–Einstein surfaces

Daniel Guan

Vol. 288 (2017), No. 2, 343–353
Abstract

We prove a conjecture on the pinching of the bisectional curvature of nonpositively curved Kähler–Einstein surfaces. We also prove that any compact Kähler–Einstein surface M is a quotient of the complex two-dimensional unit ball or the complex two-dimensional plane if M has nonpositive Einstein constant and, at each point, the average holomorphic sectional curvature is closer to the minimum than to the maximum.

Keywords
Kähler–Einstein metrics, compact complex surfaces, bisectional curvature, pinching of the curvatures
Mathematical Subject Classification 2010
Primary: 32M15, 32Q20, 53C21, 53C55
Milestones
Received: 8 December 2014
Revised: 1 December 2016
Accepted: 14 December 2016
Published: 28 April 2017
Authors
Daniel Guan
Department of Mathematics
The University of California at Riverside
Riverside, CA 92521
United States