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Characterizations of the complex projective plane by curvature


Authors: Robert E. Greene and Harsh Pittie
Journal: Proc. Amer. Math. Soc. 49 (1975), 131-134
MSC: Primary 32C10; Secondary 53C55
DOI: https://doi.org/10.1090/S0002-9939-1975-0387650-1
MathSciNet review: 0387650
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Abstract: We give short proofs to show that under various positivity assumptions on the curvature of a Kähler surface $ X$, it is biholomorphically equivalent to $ {P_2}(C)$. In particular, the case of $ \delta $-holomorphic pinching $ > 1/2$ (Theorem 1) is best possible and, we believe, new.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0387650-1
Keywords: Kähler manifold, curvature, pinching, Chern class, Pontrjagin class, Riemann-Roch, Kodaira vanishing theorem
Article copyright: © Copyright 1975 American Mathematical Society

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