Quadric hypersurfaces of finite type
Bang-Yen Chen, Franki Dillen, Hong-Zao Song (1992)
Colloquium Mathematicae
Similarity:
Bang-Yen Chen, Franki Dillen, Hong-Zao Song (1992)
Colloquium Mathematicae
Similarity:
Vladimir E. Shklover (2000)
Revista Matemática Iberoamericana
Similarity:
The Schiffer Problem as originally stated for Euclidean spaces (and later for some symmetric spaces) is the following: Given a bounded connected open set Ω with a regular boundary and such that the complement of its closure is connected, does the existence of a solution to the Overdetermined Neumann Problem (N) imply that Ω is a ball? The same question for the Overdetermined Dirichlet Problem (D). We consider the generalization of the Schiffer problem to an arbitrary Riemannian manifold...
Toshiaki Adachi, Sadahiro Maeda (2006)
Colloquium Mathematicae
Similarity:
We characterize Clifford hypersurfaces and Cartan minimal hypersurfaces in a sphere by some properties of extrinsic shapes of their geodesics.
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.
Gregory Galloway (1997)
Banach Center Publications
Similarity:
Toshiaki Adachi, Sadahiro Maeda (2005)
Czechoslovak Mathematical Journal
Similarity:
In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.
Xi-Ping Zhu (1994)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Similarity: