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On
the total curvature and Betti numbers of complex projective
manifolds
Joseph Ansel Hoisington |
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Geometry & Topology 26 (2022) 1–45
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DOI: 10.2140/gt.2022.26.1
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Abstract |
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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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Keywords
total curvature, complex projective manifolds, Betti number
estimates, Chern-Lashof theorems
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Mathematical Subject Classification 2010
Primary: 53C55
Secondary: 51N35, 53C65
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References |
Publication
Received: 8 August 2018
Revised: 6 May 2020
Accepted: 6 January 2021
Published: 5 April 2022
Proposed: Gang Tian
Seconded: Dan Abramovich, Frances Kirwan
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Authors |
| Joseph Ansel Hoisington | |
| Department of Mathematics University of Pennsylvania Philadelphia, PA United States |
Department of Mathematics University of Georgia Athens, GA United States |
