A d'Alembert Formula for Hopf Hypersurfaces
Abstract
A Hopf hypersurface in complex hyperbolic space CHn 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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