Lorentzian isoparametric hypersurfaces

Principal Curvatures of Isoparametric Hypersurfaces in Cp

Let M be an isoparametric hypersurface in CPn, and M the inverse image of M under the Hopf map. By using the relationship between the eigenvalues of the shape operators of M and M , we prove that M is homogeneous if and only if either g or l is constant, where g is the number of distinct principal curvatures of M and l is the number of non-horizontal eigenspaces of the shape operator on M .

Hypersurfaces of Prescribed Curvature in Lorentzian Manifolds

The existence of closed hypersurfaces of prescribed curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers.

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Planar Normal Sections on Isoparametric Hypersurfaces and the Infinity Laplacian

We present a new characterization of Cartan isoparametric hypersurfaces in terms of properties of the polynomial that determines the algebraic set of planar normal sections on the homogeneous isoparametric hypersurfaces in spheres. We show that Cartan isoparametric hypersurfaces are the only homogeneous isoparametric hypersurfaces in spheres for which the infinity Laplacian of the polynomial th...

Triality and the Normal Sections of Cartan’s Isoparametric Hypersurfaces

The present paper is devoted to study the algebraic sets of normal sections of the so called Cartan’s isoparametric hypersurfaces MR, MC, MH and MO of complete flags in the projective planes RP , CP , HP 2 and OP . It presents a connection between “normed trialities” and the polynomial defining the algebraic sets of normal sections of these hypersurfaces. It contains also a geometric and topolo...