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arXiv · 0912.0649

A d'Alembert Formula for Hopf Hypersurfaces

Thomas A. Ivey
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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.

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Thomas A. Ivey. 2009-12-03. A d'Alembert Formula for Hopf Hypersurfaces. https://arxiv.org/abs/0912.0649

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