On manifolds with nonnegative curvature on totally isotropic 2-planes

W Seaman

doi:10.1090/S0002-9947-1993-1123458-2

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On manifolds with nonnegative curvature on totally isotropic 2-planes

Journal article

Open access

Peer reviewed

On manifolds with nonnegative curvature on totally isotropic 2-planes

W Seaman

Transactions of the American Mathematical Society, Vol.338(2), pp.843-855

1993

DOI: 10.1090/S0002-9947-1993-1123458-2

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Abstract

We prove that a compact orientable 2n-dimensional Riemannian manifold, with second Betti number nonzero, nonnegative curvature on totally isotropic 2-planes, and satisfying a positivity-type condition at one point, is necessarily Kahler, with second Betti number 1. Using the methods of Siu and Yau, we prove that if the positivity condition is satisfied at every point, then the manifold is biholomorphic to complex projective space.

Differential Geometry

Geometry

Mathematics

Exact sciences and technology

Sciences and techniques of general use

Details

Title: Subtitle: On manifolds with nonnegative curvature on totally isotropic 2-planes
Creators: W Seaman - Univ. Iowa, dep. mathematics, Iowa City IA 52242, United States
Resource Type: Journal article
Publication Details: Transactions of the American Mathematical Society, Vol.338(2), pp.843-855
DOI: 10.1090/S0002-9947-1993-1123458-2
ISSN: 0002-9947
eISSN: 1088-6850
Publisher: American Mathematical Society
Language: English
Date published: 1993
Academic Unit: Mathematics
Record Identifier: 9984241050102771

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