Kaehler submanifolds with parallel pluri-mean curvature

Details Kaehler submanifolds with parallel pluri-mean curvature Kaehler submanifolds with parallel pluri-mean curvature

2001-11-20

arxiv.org/abs/math/0111217v1

Differential Geom. Appl. 20 (2004) 46-66

Mathematics

Differential Geometry

Plain TeX, 21 pages

Scientific paper

10.1016/S0926-2245(03)00055-X

We investigate the local geometry of a class of K\"ahler submanifolds $M \subset \R^n$ which generalize surfaces of constant mean curvature. The role of the mean curvature vector is played by the $(1,1)$-part (i.e. the $dz_id\bar z_j$-components) of the second fundamental form $\alpha$, which we call the pluri-mean curvature. We show that these K\"ahler submanifolds are characterized by the existence of an associated family of isometric submanifolds with rotated second fundamental form. Of particular interest is the isotropic case where this associated family is trivial. We also investigate the properties of the corresponding Gauss map which is pluriharmonic.

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