Displaying similar documents to “Real hypersurfaces with an induced almost contact structure”

A certain tensor on real hypersurfaces in a nonflat complex space form

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 ( φ , ξ , η , g ) 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 h ( = 1 2 ξ φ ) plays an important role in contact Riemannian geometry. In this...

A short note on f -biharmonic hypersurfaces

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 f -biharmonic hypersurfaces in real space forms. By using the f -biharmonic equation for a hypersurface of a Riemannian manifold, we characterize the f -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 f -biharmonic vertical cylinders in S 2 × .

Weingarten hypersurfaces of the spherical type in Euclidean spaces

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 M n , n 2 , in Euclidean space satisfying a relation r = 1 n ( - 1 ) r + 1 r f r - 1 n r H r = 0 , where H r is the r th mean curvature and f C ( M n ; ) , 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...

A characterization of a certain real hypersurface of type ( A 2 ) in a complex projective space

Byung Hak Kim, In-Bae Kim, Sadahiro Maeda (2017)

Czechoslovak Mathematical Journal

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In the class of real hypersurfaces M 2 n - 1 isometrically immersed into a nonflat complex space form M ˜ n ( c ) of constant holomorphic sectional curvature c ( 0 ) which is either a complex projective space P n ( c ) or a complex hyperbolic space H n ( c ) according as c > 0 or c < 0 , 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....

New characterizations of linear Weingarten hypersurfaces immersed in the hyperbolic space

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 n + 1 , that is, complete hypersurfaces of n + 1 whose mean curvature H and normalized scalar curvature R satisfy R = a H + b for some a , b . 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 n + 1 . Furthermore,...

A genericity theorem for algebraic stacks and essential dimension of hypersurfaces

Zinovy Reichstein, Angelo Vistoli (2013)

Journal of the European Mathematical Society

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We compute the essential dimension of the functors Forms n , d and Hypersurf n , d of equivalence classes of homogeneous polynomials in n variables and hypersurfaces in n 1 , respectively, over any base field k of characteristic 0 . Here two polynomials (or hypersurfaces) over K are considered equivalent if they are related by a linear change of coordinates with coefficients in K . Our proof is based on a new Genericity Theorem for algebraic stacks, which is of independent interest. As another application...

Spacelike intersection curve of three spacelike hypersurfaces in E 1 4

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 E 1 4 .

Lightlike hypersurfaces of an indefinite Kaehler manifold of a quasi-constant curvature

Dae Ho Jin, Jae Won Lee (2019)

Communications in Mathematics

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We study lightlike hypersurfaces M of an indefinite Kaehler manifold M ¯ of quasi-constant curvature subject to the condition that the characteristic vector field ζ of M ¯ is tangent to M . First, we provide a new result for such a lightlike hypersurface. Next, we investigate such a lightlike hypersurface M of M ¯ such that (1) the screen distribution S ( T M ) is totally umbilical or (2) M is screen conformal.

A half-space type property in the Euclidean sphere

Marco Antonio Lázaro Velásquez (2022)

Archivum Mathematicum

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We study the notion of strong r -stability for the context of closed hypersurfaces Σ n ( n 3 ) with constant ( r + 1 ) -th mean curvature H r + 1 immersed into the Euclidean sphere 𝕊 n + 1 , where r { 1 , ... , n - 2 } . In this setting, under a suitable restriction on the r -th mean curvature H r , we establish that there are no r -strongly stable closed hypersurfaces immersed in a certain region of 𝕊 n + 1 , a region that is determined by a totally umbilical sphere of 𝕊 n + 1 . We also provide a rigidity result for such hypersurfaces.

On some properties of induced almost contact structures

Zuzanna Szancer (2015)

Annales Polonici Mathematici

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Real affine hypersurfaces of the complex space n + 1 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.

Real hypersurfaces with a special transversal vector field

Zuzanna Szancer (2012)

Annales Polonici Mathematici

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Real affine hypersurfaces of the complex space n + 1 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.

The natural operators of general affine connections into general affine connections

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 f m -natural operators  transforming general affine connections on m -manifolds into general affine ones to the known description of all G L ( 𝐑 m ) -invariant maps 𝐑 m * 𝐑 m k 𝐑 m * k 𝐑 m for k = 1 , 3 .

A characterization of n-dimensional hypersurfaces in R n + 1 with commuting curvature operators

Yulian T. Tsankov (2005)

Banach Center Publications

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Let Mⁿ be a hypersurface in R n + 1 . We prove that two classical Jacobi curvature operators J x and J y 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 ( K x , y K z , u ) ( u ) = ( K z , u K x , y ) ( u ) , where K x , y ( u ) = R ( x , y , u ) , for all orthonormal tangent vectors x,y,z,w and for all points p ∈ M.

f -biminimal maps between Riemannian manifolds

Yan Zhao, Ximin Liu (2019)

Czechoslovak Mathematical Journal

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We give the definition of f -biminimal submanifolds and derive the equation for f -biminimal submanifolds. As an application, we give some examples of f -biminimal manifolds. Finally, we consider f -minimal hypersurfaces in the product space n × 𝕊 1 ( a ) and derive two rigidity theorems.

Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds

Mouhamed Moustapha Fall, Fethi Mahmoudi (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Given a domain Ω of m + 1 and a k -dimensional non-degenerate minimal submanifold K of Ω with 1 k m - 1 , we prove the existence of a family of embedded constant mean curvature hypersurfaces in Ω which as their mean curvature tends to infinity concentrate along K and intersecting Ω perpendicularly along their boundaries.

Complete noncompact submanifolds with flat normal bundle

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 n + p with flat normal bundle. We prove that if the second fundamental form A of M satisfies M i | A | α < , where α ∈ [2(1 - √(2/n)), 2(1 + √(2/n))], then M is an affine n-dimensional plane. In particular, if n ≤ 8 and M | A | d < , d = 1,3, then M is an affine n-dimensional plane. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite L α -norm curvature in ℝ⁷ are considered.

Induced almost continuous functions on hyperspaces

Alejandro Illanes (2006)

Colloquium Mathematicae

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For a metric continuum X, let C(X) (resp., 2 X ) 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 2 f : 2 X 2 Y be the induced functions given by C ( f ) ( A ) = c l Y ( f ( A ) ) and 2 f ( A ) = c l Y ( f ( A ) ) . In this paper, we prove that: • If 2 f 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]...

On strongly affine extensions of commutative rings

Nabil Zeidi (2020)

Czechoslovak Mathematical Journal

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A ring extension R S is said to be strongly affine if each R -subalgebra of S is a finite-type R -algebra. In this paper, several characterizations of strongly affine extensions are given. For instance, we establish that if R is a quasi-local ring of finite dimension, then R S is integrally closed and strongly affine if and only if R S is a Prüfer extension (i.e. ( R , S ) is a normal pair). As a consequence, the equivalence of strongly affine extensions, quasi-Prüfer extensions and INC-pairs is shown....