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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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  • [1] M. Berger, P. Gauduchon et E. Mazet, Le spectre d'une variete Riemannienne, Lecture Notes in Math., vol. 194, Springer-Verlag, New York, 1971. MR 0282313 (43:8025)
  • [2] C. J. Ferraris, On Kähler manifolds with positive curvature, J. Differential Geometry 11 (1976), 133-146. MR 0405304 (53:9098)
  • [3] R. E. Greene and H. Wu, Curvature and complex analysis, Bull. Amer. Math. Soc. 77 (1971), 1045-1049. MR 0283240 (44:473)
  • [4] P. F. Klembeck, Function theory on complete open Hermitian manifolds, Thesis, Univ. of California, Los Angeles, 1975.

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Keywords: Riemannian manifold, Hermitian manifold, sectional curvature, complex analytic subvariety, "blowing-up", protective tangent cone
Article copyright: © Copyright 1979 American Mathematical Society

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