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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On manifolds with nonnegative curvature on totally isotropic 2-planes


Author: Walter Seaman
Journal: Trans. Amer. Math. Soc. 338 (1993), 843-855
MSC: Primary 53C21; Secondary 53C42
DOI: https://doi.org/10.1090/S0002-9947-1993-1123458-2
MathSciNet review: 1123458
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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 Kähler, 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.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1123458-2
Article copyright: © Copyright 1993 American Mathematical Society

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