A d'Alembert Formula for Hopf Hypersurfaces
Differential Geometry
2010-11-29 v2
Abstract
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.
Cite
@article{arxiv.0912.0649,
title = {A d'Alembert Formula for Hopf Hypersurfaces},
author = {Thomas A. Ivey},
journal= {arXiv preprint arXiv:0912.0649},
year = {2010}
}
Comments
14 pages; revised version includes formula for arbitrary n