On some properties of induced almost contact structures

Zuzanna Szancer

Displaying similar documents to “On some properties of induced almost contact structures”

Real hypersurfaces with an induced almost contact structure

Michał Szancer, Zuzanna Szancer (2009)

Colloquium Mathematicae

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We study real affine hypersurfaces $f : M \to ℂ^{n + 1}$ with an almost contact structure (φ,ξ,η) induced by any J-tangent transversal vector field. The main purpose of this paper is to show that if (φ,ξ,η) is metric relative to the second fundamental form then it is Sasakian and moreover f(M) is a piece of a hyperquadric in $ℝ^{2 n + 2}$ .

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 $ℂ^{n + 1}$ 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.

Real hypersurfaces with parallel induced almost contact structures

Zuzanna Szancer (2012)

Annales Polonici Mathematici

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Real affine hypersurfaces of the complex space $ℂ^{n + 1}$ with a J-tangent transversal vector field and an induced almost contact structure (φ,ξ,η) are studied. Some properties of hypersurfaces with φ or η parallel relative to an induced connection are proved. Also a local characterization of these hypersurfaces is given.

The almost Daugavet property and translation-invariant subspaces

Simon Lücking (2014)

Colloquium Mathematicae

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Let G be a metrizable, compact abelian group and let Λ be a subset of its dual group Ĝ. We show that $C_{Λ} (G)$ has the almost Daugavet property if and only if Λ is an infinite set, and that $L ¹_{Λ} (G)$ has the almost Daugavet property if and only if Λ is not a Λ(1) set.

A local characterization of affine holomorphic immersions with an anti-complex and ∇-parallel shape operator

Maria Robaszewska (2002)

Annales Polonici Mathematici

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We study the complex hypersurfaces $f : M^{(n)} \to ℂ^{n + 1}$ which together with their transversal bundles have the property that around any point of M there exists a local section of the transversal bundle inducing a ∇-parallel anti-complex shape operator S. We give a class of examples of such hypersurfaces with an arbitrary rank of S from 1 to [n/2] and show that every such hypersurface with positive type number and S ≠ 0 is locally of this kind, modulo an affine isomorphism of $ℂ^{n + 1}$ .

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 $h$ $(= \frac{1}{2} ℒ_{ξ} φ)$ plays an important role in contact Riemannian geometry. In this...

A characterization of almost continuity and weak continuity

Chrisostomos Petalas, Theodoros Vidalis (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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It is well known that a function $f$ from a space $X$ into a space $Y$ is continuous if and only if, for every set $K$ in $X$ the image of the closure of $K$ under $f$ is a subset of the closure of the image of it. In this paper we characterize almost continuity and weak continuity by proving similar relations for the subsets $K$ of $X$ .

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 $2^{f} : 2^{X} \to 2^{Y}$ 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]...

Hypersurfaces with almost complex structures in the real affine space

Mayuko Kon (2007)

Colloquium Mathematicae

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We study affine hypersurface immersions $f : M \to ℝ^{2 n + 1}$ , where M is an almost complex n-dimensional manifold. The main purpose is to give a condition for (M,J) to be a special Kähler manifold with respect to the Levi-Civita connection of an affine fundamental form.

A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems

Robert Krawczyk (2014)

Banach Center Publications

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In this work we will be concerned with the existence of almost homoclinic solutions for a Newtonian system $q ̈ + \nabla_{q} V (t, q) = f (t)$ , where t ∈ ℝ, q ∈ ℝⁿ. It is assumed that a potential V: ℝ × ℝⁿ → ℝ is C¹-smooth and its gradient map $\nabla_{q} V : ℝ \times ℝ ⁿ \to ℝ ⁿ$ is bounded with respect to t. Moreover, a forcing term f: ℝ → ℝⁿ is continuous, bounded and square integrable. We will show that the approximative scheme due to J. Janczewska (see [J2]) for a time periodic potential extends to our case.

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 $ℳ f_{m}$ -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 $𝐑^{m *} \otimes 𝐑^{m} \to \otimes^{k} 𝐑^{m *} \otimes \otimes^{k} 𝐑^{m}$ for $k = 1, 3$ .

On Some Family of Contractible Hypersurfaces in $C^{4}$

S. Kaliman, L. Makar-Limanov (1993)

Cours de l'institut Fourier

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Almost Prüfer v-multiplication domains and the ring $D + X D_{S} [X]$

Qing Li (2010)

Colloquium Mathematicae

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This paper is a continuation of the investigation of almost Prüfer v-multiplication domains (APVMDs) begun by Li [Algebra Colloq., to appear]. We show that an integral domain D is an APVMD if and only if D is a locally APVMD and D is well behaved. We also prove that D is an APVMD if and only if the integral closure D̅ of D is a PVMD, D ⊆ D̅ is a root extension and D is t-linked under D̅. We introduce the notion of an almost t-splitting set. $D^{(S)}$ denotes the ring $D + X D_{S} [X]$ , where S is a multiplicatively...

Asymmetric tie-points and almost clopen subsets of $ℕ^{*}$

Alan S. Dow, Saharon Shelah (2018)

Commentationes Mathematicae Universitatis Carolinae

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A tie-point of compact space is analogous to a cut-point: the complement of the point falls apart into two relatively clopen non-compact subsets. We review some of the many consistency results that have depended on the construction of tie-points of $ℕ^{*}$ . One especially important application, due to Veličković, was to the existence of nontrivial involutions on $ℕ^{*}$ . A tie-point of $ℕ^{*}$ has been called symmetric if it is the unique fixed point of an involution. We define the notion of an almost...

Remotely $c$ -almost periodic type functions in $ℝ^{n}$

Marco Kostić, Vipin Kumar (2022)

Archivum Mathematicum

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In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely $c$ -almost periodic functions in $ℝ^{n},$ slowly oscillating functions in $ℝ^{n},$ and further analyze the recently introduced class of quasi-asymptotically $c$ -almost periodic...

Comparing the closed almost disjointness and dominating numbers

Dilip Raghavan, Saharon Shelah (2012)

Fundamenta Mathematicae

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We prove that if there is a dominating family of size ℵ₁, then there are ℵ₁ many compact subsets of $ω^{ω}$ whose union is a maximal almost disjoint family of functions that is also maximal with respect to infinite partial functions.

Special sets of reals and weak forms of normality on Isbell--Mrówka spaces

Vinicius de Oliveira Rodrigues, Victor dos Santos Ronchim, Paul J. Szeptycki (2023)

Commentationes Mathematicae Universitatis Carolinae

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We recall some classical results relating normality and some natural weakenings of normality in $Ψ$ -spaces over almost disjoint families of branches in the Cantor tree to special sets of reals like $Q$ -sets, $λ$ -sets and $σ$ -sets. We introduce a new class of special sets of reals which corresponds to the corresponding almost disjoint family of branches being $ℵ_{0}$ -separated. This new class fits between $λ$ -sets and perfectly meager sets. We also discuss conditions for an almost disjoint family $𝒜$ being...

Isotropic almost complex structures and harmonic unit vector fields

Amir Baghban, Esmaeil Abedi (2018)

Archivum Mathematicum

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Isotropic almost complex structures $J_{δ, σ}$ define a class of Riemannian metrics $g_{δ, σ}$ on tangent bundles of Riemannian manifolds which are a generalization of the Sasaki metric. In this paper, some results will be obtained on the integrability of these almost complex structures and the notion of a harmonic unit vector field will be introduced with respect to the metrics $g_{δ, 0}$ . Furthermore, the necessary and sufficient conditions for a unit vector field to be a harmonic unit vector field will be obtained. ...

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 $M^{n}$ , $n \geq 2$ , in Euclidean space satisfying a relation $\sum_{r = 1}^{n} {(- 1)}^{r + 1} r f^{r - 1} (\binom{n}{r}) H_{r} = 0,$ where $H_{r}$ is the $r$ th mean curvature and $f \in C^{\infty} (M^{n}; ℝ)$ , 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 class of $I_{0}$ -sets

David Grow (1987)

Colloquium Mathematicae

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Almost multiplicative functions on commutative Banach algebras

S. H. Kulkarni, D. Sukumar (2010)

Studia Mathematica

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Let A be a complex commutative Banach algebra with unit 1 and δ > 0. A linear map ϕ: A → ℂ is said to be δ-almost multiplicative if |ϕ(ab) - ϕ(a)ϕ(b)| ≤ δ||a|| ||b|| for all a,b ∈ A. Let 0 < ϵ < 1. The ϵ-condition spectrum of an element a in A is defined by $σ_{ϵ} (a) : = λ \in ℂ : | | λ - {a | | | | (λ - a)}^{- 1} | | \geq 1 / ϵ$ with the convention that $| | λ - {a | | | | (λ - a)}^{- 1} | | = \infty$ when λ - a is not invertible. We prove the following results connecting these two notions: (1) If ϕ(1) = 1 and ϕ is δ-almost multiplicative, then $ϕ (a) \in σ_{δ} (a)$ for all a in A. (2) If ϕ is linear and $ϕ (a) \in σ_{ϵ} (a)$ for...

On almost cosymplectic (κ,μ,ν)-spaces

Piotr Dacko, Zbigniew Olszak (2005)

Banach Center Publications

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An almost cosymplectic (κ,μ,ν)-space is by definition an almost cosymplectic manifold whose structure tensor fields φ, ξ, η, g satisfy a certain special curvature condition (see formula (eq1b)). This condition is invariant with respect to the so-called -homothetic transformations of almost cosymplectic structures. For such manifolds, the tensor fields φ, h ( $= (1 / 2) ℒ_{ξ} φ$ ), A ( = -∇ξ) fulfill a certain system of differential equations. It is proved that the leaves of the canonical foliation of an...

Bi-Legendrian connections

Beniamino Cappelletti Montano (2005)

Annales Polonici Mathematici

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We define the concept of a bi-Legendrian connection associated to a bi-Legendrian structure on an almost -manifold $M^{2 n + r}$ . Among other things, we compute the torsion of this connection and prove that the curvature vanishes along the leaves of the bi-Legendrian structure. Moreover, we prove that if the bi-Legendrian connection is flat, then the bi-Legendrian structure is locally equivalent to the standard structure on $ℝ^{2 n + r}$ .