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Kähler manifolds with curvature bounded from above by a decreasing function


Author: Mitsuhiro Itoh
Journal: Proc. Amer. Math. Soc. 75 (1979), 289-293
MSC: Primary 53C20; Secondary 32E10, 32F30, 53C55
DOI: https://doi.org/10.1090/S0002-9939-1979-0532153-8
MathSciNet review: 532153
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Abstract: Let M be a simply connected complete Kähler manifold. If M has curvature bounded from above by a certain positive decreasing function, then it is a Stein manifold, diffeomorphic to a euclidean space. This fact is a generalization of the well-known propositions for complete manifolds of nonpositive curvature and is shown by the aid of a Rauch comparison theorem for conjugate points together with a comparison theorem of Siu and Yau with respect to the Hessian of distance functions.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0532153-8
Keywords: Sectional curvature, comparison theorem, Stein manifold
Article copyright: © Copyright 1979 American Mathematical Society

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