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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On subvarieties of a Hermitian manifold


Author: Carlos J. Ferraris
Journal: Proc. Amer. Math. Soc. 73 (1979), 237-243
MSC: Primary 53C55; Secondary 32C25
MathSciNet review: 516471
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Abstract: We make use of the variational properties of the geodesic distance function of a Riemannian manifold and the technique of the ``blowing-up'' ($ \sigma $-process) on a complex manifold to derive the nonexistence of compact complex analytic subvarieties in a simply connected, complete Hermitian manifold with nonpositive sectional curvature.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0516471-5
PII: S 0002-9939(1979)0516471-5
Keywords: Riemannian manifold, Hermitian manifold, sectional curvature, complex analytic subvariety, "blowing-up", protective tangent cone
Article copyright: © Copyright 1979 American Mathematical Society