On subvarieties of a Hermitian manifold
HTML articles powered by AMS MathViewer
- by Carlos J. Ferraris PDF
- Proc. Amer. Math. Soc. 73 (1979), 237-243 Request permission
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.References
- Marcel Berger, Paul Gauduchon, and Edmond Mazet, Le spectre d’une variété riemannienne, Lecture Notes in Mathematics, Vol. 194, Springer-Verlag, Berlin-New York, 1971 (French). MR 0282313
- C. J. Ferraris, Kähler manifolds with positive curvature, J. Differential Geometry 11 (1976), no. 1, 133–146. MR 405304
- R. E. Greene and H. Wu, Curvature and complex analysis, Bull. Amer. Math. Soc. 77 (1971), 1045–1049. MR 283240, DOI 10.1090/S0002-9904-1971-12856-2 P. F. Klembeck, Function theory on complete open Hermitian manifolds, Thesis, Univ. of California, Los Angeles, 1975.
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 237-243
- MSC: Primary 53C55; Secondary 32C25
- DOI: https://doi.org/10.1090/S0002-9939-1979-0516471-5
- MathSciNet review: 516471