A d'Alembert Formula for Hopf Hypersurfaces

Details A d'Alembert Formula for Hopf Hypersurfaces A d'Alembert Formula for Hopf Hypersurfaces

2009-12-03

arxiv.org/abs/0912.0649v2

Mathematics

Differential Geometry

14 pages; revised version includes formula for arbitrary n

Scientific paper

A Hopf hypersurface in complex hyperbolic space CH^n is one in which the complex structure applied to the normal vector is a principal direction at each point. In this paper, Hopf hypersurfaces for which the corresponding principal curvature is small (relative to the ambient sectional curvature) are studied by means of a generalized Gauss map into a product of spheres, and it is shown that the hypersurface may be recovered from the image of this map, via an explicit formula.

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