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On the total curvature and Betti numbers of complex projective manifolds

Joseph Ansel Hoisington

Geometry & Topology 26 (2022) 1–45
DOI: 10.2140/gt.2022.26.1

We prove an inequality between the sum of the Betti numbers of a complex projective manifold and its total curvature, and we characterize the complex projective manifolds whose total curvature is minimal. These results extend the classical theorems of Chern and Lashof to complex projective space.

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total curvature, complex projective manifolds, Betti number estimates, Chern-Lashof theorems
Mathematical Subject Classification 2010
Primary: 53C55
Secondary: 51N35, 53C65
Received: 8 August 2018
Revised: 6 May 2020
Accepted: 6 January 2021
Published: 5 April 2022
Proposed: Gang Tian
Seconded: Dan Abramovich, Frances Kirwan
Joseph Ansel Hoisington
Department of Mathematics
University of Pennsylvania
Philadelphia, PA
United States
Department of Mathematics
University of Georgia
Athens, GA
United States