Displaying similar documents to “Geodesics and circles on real hypersurfaces of type A and B in a complex space form.”

A Useful Characterization of Some Real Hypersurfaces in a Nonflat Complex Space Form

Takehiro Itoh, Sadahiro Maeda (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We characterize totally η-umbilic real hypersurfaces in a nonflat complex space form M̃ₙ(c) (= ℂPⁿ(c) or ℂHⁿ(c)) and a real hypersurface of type (A₂) of radius π/(2√c) in ℂPⁿ(c) by observing the shape of some geodesics on those real hypersurfaces as curves in the ambient manifolds (Theorems 1 and 2).

On the hypersurfaces contained in their Hessian

Pietro De Poi, Giovanna Ilardi (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Similarity:

This article presents the theory of focal locus applied to the hypersurfaces in the projective space which are (finitely) covered by linear spaces and such that the tangent space is constant along these spaces.

On the quadric CMC spacelike hypersurfaces in Lorentzian space forms

Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos (2016)

Colloquium Mathematicae

Similarity:

We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.

Parallel hypersurfaces

Barbara Opozda, Udo Simon (2014)

Annales Polonici Mathematici

Similarity:

We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.