Real hypersurfaces of Kahler manifolds.

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