Some Classes of Lorentzian $\alpha $-Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection

Santu DEY; Buddhadev Pal; Arindam BHATTACHARYYA

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Displaying similar documents to “Some Classes of Lorentzian $α$ -Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection”

The Killing Tensors on an $n$ -dimensional Manifold with $S L (n,)$ -structure

Sergey E. Stepanov, Irina I. Tsyganok, Marina B. Khripunova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an $n$ -dimensional differentiable manifold $M$ endowed with an equiaffine $S L (n,)$ -structure and discuss possible applications of obtained results in Riemannian geometry.

On a Semi-symmetric Metric Connection in an Almost Kenmotsu Manifold with Nullity Distributions

Gopal Ghosh, Uday Chand De (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We consider a semisymmetric metric connection in an almost Kenmotsu manifold with its characteristic vector field $ξ$ belonging to the ${(k, μ)}^{'}$ -nullity distribution and $(k, μ)$ -nullity distribution respectively. We first obtain the expressions of the curvature tensor and Ricci tensor with respect to the semisymmetric metric connection in an almost Kenmotsu manifold with $ξ$ belonging to ${(k, μ)}^{'}$ - and $(k, μ)$ -nullity distribution respectively. Then we characterize an almost Kenmotsu manifold with $ξ$ belonging to ${(k, μ)}^{'}$ -nullity...

On the classification of $3$ -dimensional $F$ -manifold algebras

Zhiqi Chen, Jifu Li, Ming Ding (2022)

Czechoslovak Mathematical Journal

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$F$ -manifold algebras are focused on the algebraic properties of the tangent sheaf of $F$ -manifolds. The local classification of 3-dimensional $F$ -manifolds has been given in A. Basalaev, C. Hertling (2021). We study the classification of 3-dimensional $F$ -manifold algebras over the complex field $ℂ$ .

$η$ -Ricci Solitons on $η$ -Einstein ${(L C S)}_{n}$ -Manifolds

Shyamal Kumar Hui, Debabrata Chakraborty (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The object of the present paper is to study $η$ -Ricci solitons on $η$ -Einstein ${(L C S)}_{n}$ -manifolds. It is shown that if $ξ$ is a recurrent torse forming $η$ -Ricci soliton on an $η$ -Einstein ${(L C S)}_{n}$ -manifold then $ξ$ is (i) concurrent and (ii) Killing vector field.

Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms

Shyamal K. Hui, Richard S. Lemence, Pradip Mandal (2020)

Commentationes Mathematicae Universitatis Carolinae

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A submanifold $M^{m}$ of a generalized Sasakian-space-form ${\bar{M}}^{2 n + 1} (f_{1}, f_{2}, f_{3})$ is said to be $C$ -totally real submanifold if $ξ \in Γ (T^{⊥} M)$ and $φ X \in Γ (T^{⊥} M)$ for all $X \in Γ (T M)$ . In particular, if $m = n$ , then $M^{n}$ is called Legendrian submanifold. Here, we derive Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms with respect to different connections; namely, quarter symmetric metric connection, Schouten-van Kampen connection and Tanaka-Webster connection.

Some type of semisymmetry on two classes of almost Kenmotsu manifolds

Dibakar Dey, Pradip Majhi (2021)

Communications in Mathematics

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The object of the present paper is to study some types of semisymmetry conditions on two classes of almost Kenmotsu manifolds. It is shown that a $(k, μ)$ -almost Kenmotsu manifold satisfying the curvature condition $Q \cdot R = 0$ is locally isometric to the hyperbolic space $ℍ^{2 n + 1} (- 1)$ . Also in $(k, μ)$ -almost Kenmotsu manifolds the following conditions: (1) local symmetry $(\nabla R = 0)$ , (2) semisymmetry $(R \cdot R = 0)$ , (3) $Q (S, R) = 0$ , (4) $R \cdot R = Q (S, R)$ , (5) locally isometric to the hyperbolic space $ℍ^{2 n + 1} (- 1)$ are equivalent. Further, it is proved that a ${(k, μ)}^{'}$ -almost Kenmotsu manifold...

Remarks on the behaviour of higher-order derivations on the gluing of differential spaces

Krzysztof Drachal (2015)

Czechoslovak Mathematical Journal

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This paper is about some geometric properties of the gluing of order $k$ in the category of Sikorski differential spaces, where $k$ is assumed to be an arbitrary natural number. Differential spaces are one of possible generalizations of the concept of an infinitely differentiable manifold. It is known that in many (very important) mathematical models, the manifold structure breaks down. Therefore it is important to introduce a more general concept. In this paper, in particular, the behaviour...

On canonical constructions on connections

Jan Kurek, Włodzimierz Mikulski (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We study how a projectable general connection $Γ$ in a 2-fibred manifold $Y^{2} \to Y^{1} \to Y^{0}$ and a general vertical connection $Θ$ in $Y^{2} \to Y^{1} \to Y^{0}$ induce a general connection $A (Γ, Θ)$ in $Y^{2} \to Y^{1}$ .

The vertical prolongation of the projectable connections

Anna Bednarska (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We prove that any first order $ℱ_{2} ℳ_{m_{1}, m_{2}, n_{1}, n_{2}}$ -natural operator transforming projectable general connections on an $(m_{1}, m_{2}, n_{1}, n_{2})$ -dimensional fibred-fibred manifold $p = (p, p) : (p_{Y} : Y \to Y) \to (p_{M} : M \to M)$ into general connections on the vertical prolongation $V Y \to M$ of $p : Y \to M$ is the restriction of the (rather well-known) vertical prolongation operator $𝒱$ lifting general connections $\bar{Γ}$ on a fibred manifold $Y \to M$ into $𝒱 \bar{Γ}$ (the vertical prolongation of $\bar{Γ}$ ) on $V Y \to M$ .

Approximately Einstein ACH metrics, volume renormalization, and an invariant for contact manifolds

Neil Seshadri (2009)

Bulletin de la Société Mathématique de France

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To any smooth compact manifold $M$ endowed with a contact structure $H$ and partially integrable almost CR structure $J$ , we prove the existence and uniqueness, modulo high-order error terms and diffeomorphism action, of an approximately Einstein ACH (asymptotically complex hyperbolic) metric $g$ on $M \times (- 1, 0)$ . We consider the asymptotic expansion, in powers of a special defining function, of the volume of $M \times (- 1, 0)$ with respect to $g$ and prove that the log term coefficient is independent of $J$ (and any choice...

Displaying similar documents to “Some Classes of Lorentzian α -Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection”

Displaying similar documents to “Some Classes of Lorentzian $α$ -Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection”