Real hypersurfaces of Kahler manifolds

Klingenberg, W.

Abstract

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 $T^{1,0}(C^n)$.

Citation

Klingenberg, W. (2001). Real hypersurfaces of Kahler manifolds. Asian Journal of Mathematics, 5(1), 1 -18. https://doi.org/10.4310/ajm.2001.v5.n1.a1

• 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
• DOI: https://doi.org/10.4310/ajm.2001.v5.n1.a1
• Publisher URL: http://www.ims.cuhk.edu.hk/~ajm/