On Some Family of Contractible Hypersurfaces in
S. Kaliman, L. Makar-Limanov (1993)
Cours de l'institut Fourier
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S. Kaliman, L. Makar-Limanov (1993)
Cours de l'institut Fourier
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Kazuhiro Okumura (2020)
Czechoslovak Mathematical Journal
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In a nonflat complex space form (namely, a complex projective space or a complex hyperbolic space), real hypersurfaces admit an almost contact metric structure induced from the ambient space. As a matter of course, many geometers have investigated real hypersurfaces in a nonflat complex space form from the viewpoint of almost contact metric geometry. On the other hand, it is known that the tensor field plays an important role in contact Riemannian geometry. In this...
Selcen Y. Perktaş, Bilal E. Acet, Adara M. Blaga (2020)
Commentationes Mathematicae Universitatis Carolinae
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In the present paper we give some properties of -biharmonic hypersurfaces in real space forms. By using the -biharmonic equation for a hypersurface of a Riemannian manifold, we characterize the -biharmonicity of constant mean curvature and totally umbilical hypersurfaces in a Riemannian manifold and, in particular, in a real space form. As an example, we consider -biharmonic vertical cylinders in .
Cid D. F. Machado, Carlos M. C. Riveros (2020)
Commentationes Mathematicae Universitatis Carolinae
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We generalize a parametrization obtained by A. V. Corro in (2006) in the three-dimensional Euclidean space. Using this parametrization we study a class of oriented hypersurfaces , , in Euclidean space satisfying a relation where is the th mean curvature and , these hypersurfaces are called Weingarten hypersurfaces of the spherical type. This class of hypersurfaces includes the surfaces of the spherical type (Laguerré minimal surfaces). We characterize these hypersurfaces in terms...
Byung Hak Kim, In-Bae Kim, Sadahiro Maeda (2017)
Czechoslovak Mathematical Journal
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In the class of real hypersurfaces isometrically immersed into a nonflat complex space form of constant holomorphic sectional curvature which is either a complex projective space or a complex hyperbolic space according as or , there are two typical examples. One is the class of all real hypersurfaces of type (A) and the other is the class of all ruled real hypersurfaces. Note that the former example are Hopf manifolds and the latter are non-Hopf manifolds....
Cícero P. Aquino, Henrique F. de Lima (2015)
Archivum Mathematicum
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In this paper, we deal with complete linear Weingarten hypersurfaces immersed in the hyperbolic space , that is, complete hypersurfaces of whose mean curvature and normalized scalar curvature satisfy for some , . In this setting, under appropriate restrictions on the mean curvature and on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of . Furthermore,...
Zinovy Reichstein, Angelo Vistoli (2013)
Journal of the European Mathematical Society
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We compute the essential dimension of the functors Forms and Hypersurf of equivalence classes of homogeneous polynomials in variables and hypersurfaces in , respectively, over any base field of characteristic . Here two polynomials (or hypersurfaces) over are considered equivalent if they are related by a linear change of coordinates with coefficients in . Our proof is based on a new Genericity Theorem for algebraic stacks, which is of independent interest. As another application...
B. Uyar Duldul, M. Caliskan (2013)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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In this paper, we compute the Frenet vectors and the curvatures of the spacelike intersection curve of three spacelike hypersurfaces given by their parametric equations in four-dimensional Minkowski space .
Dae Ho Jin, Jae Won Lee (2019)
Communications in Mathematics
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We study lightlike hypersurfaces of an indefinite Kaehler manifold of quasi-constant curvature subject to the condition that the characteristic vector field of is tangent to . First, we provide a new result for such a lightlike hypersurface. Next, we investigate such a lightlike hypersurface of such that (1) the screen distribution is totally umbilical or (2) is screen conformal.
Dirk Siersma (1988)
Banach Center Publications
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Marco Antonio Lázaro Velásquez (2022)
Archivum Mathematicum
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We study the notion of strong -stability for the context of closed hypersurfaces () with constant -th mean curvature immersed into the Euclidean sphere , where . In this setting, under a suitable restriction on the -th mean curvature , we establish that there are no -strongly stable closed hypersurfaces immersed in a certain region of , a region that is determined by a totally umbilical sphere of . We also provide a rigidity result for such hypersurfaces.
Thomas Hasanis (1984)
Colloquium Mathematicae
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Zuzanna Szancer (2015)
Annales Polonici Mathematici
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Real affine hypersurfaces of the complex space with a J-tangent transversal vector field and an induced almost contact structure (φ,ξ,η) are studied. Some properties of the induced almost contact structures are proved. In particular, we prove some properties of the induced structure when the distribution is involutive. Some constraints on a shape operator when the induced almost contact structure is either normal or ξ-invariant are also given.
Zuzanna Szancer (2012)
Annales Polonici Mathematici
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Real affine hypersurfaces of the complex space are studied. Some properties of the structure determined by a J-tangent transversal vector field are proved. Moreover, some generalizations of the results obtained by V. Cruceanu are given.
Jan Kurek, Włodzimierz M. Mikulski (2017)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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We reduce the problem of describing all -natural operators transforming general affine connections on -manifolds into general affine ones to the known description of all -invariant maps for .
Yulian T. Tsankov (2005)
Banach Center Publications
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Let Mⁿ be a hypersurface in . We prove that two classical Jacobi curvature operators and commute on Mⁿ, n > 2, for all orthonormal pairs (x,y) and for all points p ∈ M if and only if Mⁿ is a space of constant sectional curvature. Also we consider all hypersurfaces with n ≥ 4 satisfying the commutation relation , where , for all orthonormal tangent vectors x,y,z,w and for all points p ∈ M.
Yan Zhao, Ximin Liu (2019)
Czechoslovak Mathematical Journal
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We give the definition of -biminimal submanifolds and derive the equation for -biminimal submanifolds. As an application, we give some examples of -biminimal manifolds. Finally, we consider -minimal hypersurfaces in the product space and derive two rigidity theorems.
Mouhamed Moustapha Fall, Fethi Mahmoudi (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Given a domain of and a -dimensional non-degenerate minimal submanifold of with , we prove the existence of a family of embedded constant mean curvature hypersurfaces in which as their mean curvature tends to infinity concentrate along and intersecting perpendicularly along their boundaries.
Hai-Ping Fu (2016)
Annales Polonici Mathematici
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Let Mⁿ (n ≥ 3) be an n-dimensional complete super stable minimal submanifold in with flat normal bundle. We prove that if the second fundamental form A of M satisfies , where α ∈ [2(1 - √(2/n)), 2(1 + √(2/n))], then M is an affine n-dimensional plane. In particular, if n ≤ 8 and , d = 1,3, then M is an affine n-dimensional plane. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite -norm curvature in ℝ⁷ are considered.
Alejandro Illanes (2006)
Colloquium Mathematicae
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For a metric continuum X, let C(X) (resp., ) be the hyperspace of subcontinua (resp., nonempty closed subsets) of X. Let f: X → Y be an almost continuous function. Let C(f): C(X) → C(Y) and be the induced functions given by and . In this paper, we prove that: • If is almost continuous, then f is continuous. • If C(f) is almost continuous and X is locally connected, then f is continuous. • If X is not locally connected, then there exists an almost continuous function f: X → [0,1]...
Nabil Zeidi (2020)
Czechoslovak Mathematical Journal
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A ring extension is said to be strongly affine if each -subalgebra of is a finite-type -algebra. In this paper, several characterizations of strongly affine extensions are given. For instance, we establish that if is a quasi-local ring of finite dimension, then is integrally closed and strongly affine if and only if is a Prüfer extension (i.e. is a normal pair). As a consequence, the equivalence of strongly affine extensions, quasi-Prüfer extensions and INC-pairs is shown....