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Real hypersurfaces of Kahler manifolds

Klingenberg, W.

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Building on work by S. M. Webster \ref[J. Differential Geom. 13 (1978), no. 1, 25--41; MR0520599 (80e:32015)] the author studies the geometry of the second fundamental form of a real hypersurface in a Kähler manifold. As an application he proves that a compact strictly pseudoconvex hypersurface $M\subsetC^n$ is isometric to a sphere provided that $M$ has constant horizontal mean curvature and the CR structure $T_{1,0}(M)$ is parallel in $T^{1,0}(C^n)$.


Klingenberg, W. (2001). Real hypersurfaces of Kahler manifolds. Asian Journal of Mathematics, 5(1), 1 -18.

Journal Article Type Article
Online Publication Date Jan 1, 2001
Publication Date Mar 1, 2001
Deposit Date Jul 9, 2007
Publicly Available Date Feb 22, 2011
Journal Asian Journal of Mathematics
Print ISSN 1093-6106
Publisher International Press
Peer Reviewed Peer Reviewed
Volume 5
Issue 1
Pages 1 -18
Publisher URL


Published Journal Article (215 Kb)

Copyright Statement
Copyright &copy; International Press. <br /> First published in Asian journal of mathematics 5 (1) 2001, <br /> published by International Press.

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