English

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.

Keywords

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

R2 v1 2026-06-21T14:19:12.116Z