Homogeneous hypersurfaces in complex hyperbolic spaces
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In this paper, the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces is studied and a characterization of the focal set in terms of its second fundamental form is provided.Abstract:
We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the homogeneous hypersurfaces together with their multiplicities.read more
Citations
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Polar actions on complex hyperbolic spaces
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Polar actions on complex hyperbolic spaces
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Isoparametric hypersurfaces in Damek-Ricci spaces
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Real hypersurfaces with constant principal curvatures in complex space forms
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References
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On homogeneous real hypersurfaces in a complex projective space
TL;DR: In this paper, the authors considered the problem of determining homogeneous real hypersurfaces in a complex projective space Pn(C) of complex dimension n(^>2) which are orbits under analytic subgroups of the projective unitary group PU(n-\\-\\)>.
Journal ArticleDOI
Focal sets and real hypersurfaces in complex projective space
Thomas E. Cecil,Patrick J. Ryan +1 more
TL;DR: In this paper, the location of the focal points of a real submanifold is defined in terms of its second fundamental form, and the rank of a focal map onto a sheet of focal points corresponding to a principal curvature is computed using the Codazzi equation.
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