Open AccessJournal Article
Real hypersurfaces with constant principal curvatures in complex hyperbolic space.
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In this article, a complete classification of isoparametric hypersurfaces with constant principal curvatures has been obtained in the sphere, but the classification has not been obtained until now.Abstract:
Since E. Cartan's work in the late 30's the classification problem of hypersurfaces with constant principal curvatures is known to be far from trivial. In real space forms it leads to the well-known classification problem of isoparametric hypersurfaces, which has been solved in euclidean space by T. Levi-Civita [6] and B. Segre [11] and in hyperbolic space by E. Cartan [1]; in the sphere, however, a complete classification has not been obtained until now (for essential results see [1], [2], [3], [8], [9], [10], and the literature cited there).read more
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Real hypersurfaces with two principal curvatures in complex projective and hyperbolic planes
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Characterizations of some real hypersurfaces in a complex space form in terms of lie derivative
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Trajectories for Sasakian magnetic fields on real hypersurfaces of type (B) in a complex hyperbolic space
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On proper complex equifocal submanifolds
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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-\\-\\)>.
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Real hypersurfaces and complex submanifolds in complex projective space
TL;DR: In this paper, it was shown that a complex submanifold with constant principal curvatures is an open subset of a homogeneous hypersurface if and only if it has constant curvatures and Jt is principal.