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

MathSciNet review:
1123458

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Abstract: We prove that a compact orientable -dimensional Riemannian manifold, with second Betti number nonzero, nonnegative curvature on totally isotropic -planes, and satisfying a positivity-type condition at one point, is necessarily Kähler, with second Betti number . 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