Abstract
A Hopf hypersurface in complex hyperbolic space \({\mathbb{C}{\rm H}^n}\) is one for 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 ambient 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 parametrization.
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In honor of Keti Tenenblat
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Ivey, T.A. A d’Alembert Formula for Hopf Hypersurfaces. Results. Math. 60, 293–309 (2011). https://doi.org/10.1007/s00025-011-0155-4
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DOI: https://doi.org/10.1007/s00025-011-0155-4