Non-existence of real lightlike hypersurfaces of an indefinite complex space form.
Ṣahin, Bayram, Güneṣ, Rifat (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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Ṣahin, Bayram, Güneṣ, Rifat (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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Patrick J. Ryan (1972)
Colloquium Mathematicae
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Barbara Opozda, Udo Simon (2014)
Annales Polonici Mathematici
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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.
Toshiaki Adachi, Sadahiro Maeda (2006)
Colloquium Mathematicae
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We characterize Clifford hypersurfaces and Cartan minimal hypersurfaces in a sphere by some properties of extrinsic shapes of their geodesics.
Takehiro Itoh, Sadahiro Maeda (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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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).
Kim, Hyang Sook, Pyo, Yong-Soo (1998)
Balkan Journal of Geometry and its Applications (BJGA)
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Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos (2016)
Colloquium Mathematicae
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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.
Andrew Baker, Nigel Ray (1982)
Mathematica Scandinavica
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Eudes L. de Lima, Henrique F. de Lima, Eraldo A. Jr. Lima, Adriano A. Medeiros (2017)
Commentationes Mathematicae Universitatis Carolinae
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In this paper, we extend a technique due to Romero et al. establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed into a Lorentzian Killing warped product whose Riemannian base has parabolic universal Riemannian covering. As applications, we obtain rigidity results concerning these hypersurfaces. A particular study of entire Killing graphs is also made.
Akivis, Maks A., Goldberg, Vladislav V. (1998)
Beiträge zur Algebra und Geometrie
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J.W. Bruce (1981)
Mathematica Scandinavica
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Reiko Miyaoka (1982)
Mathematische Zeitschrift
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Bert Fischer (1996)
Mathematische Zeitschrift
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Angelo Vistoli (1993)
Inventiones mathematicae
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U. Abresch (1983)
Mathematische Annalen
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Bang-Yen Chen, Franki Dillen, Hong-Zao Song (1992)
Colloquium Mathematicae
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