Jurgen Berndt, Victor Sanmartin-Lopez
Published 2018-05-25Version 1
We study submanifolds whose principal curvatures, counted with multiplicities, do not depend on the normal direction. Such submanifolds are always austere, hence minimal, and have constant principal curvatures. Well-known classes of examples include totally geodesic submanifolds, homogeneous austere hypersurfaces, and singular orbits of cohomogeneity one actions. The main purpose of this article is to present a systematic approach to the construction and classification of homogeneous submanifolds whose principal curvatures are independent of the normal direction in irreducible Riemannian symmetric spaces of non-compact type and rank greater than one.
Isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in Finsler spaces
Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane
On hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$
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