Some Properties of Lorentzian $\alpha $-Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection

Santu DEY; Arindam BHATTACHARYYA

Displaying similar documents to “Some Properties of Lorentzian $α$ -Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection”

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

Santu DEY, Buddhadev Pal, Arindam BHATTACHARYYA (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The object of the present paper is to study a quarter-symmetric metric connection in an Lorentzian $α$ -Sasakian manifold. We study some curvature properties of an Lorentzian $α$ -Sasakian manifold with respect to the quarter-symmetric metric connection. We study locally $φ$ -symmetric, $φ$ -symmetric, locally projective $φ$ -symmetric, $ξ$ -projectively flat Lorentzian $α$ -Sasakian manifold with respect to the quarter-symmetric metric connection.

Projective Curvature Tensorin 3-dimensional Connected Trans-Sasakian Manifolds

Krishnendu De, Uday Chand De (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The object of the present paper is to study $ξ$ -projectively flat and $φ$ -projectively flat 3-dimensional connected trans-Sasakian manifolds. Also we study the geometric properties of connected trans-Sasakian manifolds when it is projectively semi-symmetric. Finally, we give some examples of a 3-dimensional trans-Sasakian manifold which verifies our result.

On generalized Douglas-Weyl Randers metrics

Tayebeh Tabatabaeifar, Behzad Najafi, Mehdi Rafie-Rad (2021)

Czechoslovak Mathematical Journal

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We characterize generalized Douglas-Weyl Randers metrics in terms of their Zermelo navigation data. Then, we study the Randers metrics induced by some important classes of almost contact metrics. Furthermore, we construct a family of generalized Douglas-Weyl Randers metrics which are not $R$ -quadratic. We show that the Randers metric induced by a Kenmotsu manifold is a Douglas metric which is not of isotropic $S$ -curvature. We show that the Randers metric induced by a Kenmotsu or Sasakian...

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...

Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold

Payel Karmakar (2022)

Mathematica Bohemica

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The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, $ξ$ -projectively flat, $M$ -projectively flat, $ξ$ - $M$ -projectively flat, pseudo projectively flat and $ξ$ -pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on...

Classification of $4$ -dimensional homogeneous weakly Einstein manifolds

Teresa Arias-Marco, Oldřich Kowalski (2015)

Czechoslovak Mathematical Journal

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Y. Euh, J. Park and K. Sekigawa were the first authors who defined the concept of a weakly Einstein Riemannian manifold as a modification of that of an Einstein Riemannian manifold. The defining formula is expressed in terms of the Riemannian scalar invariants of degree two. This concept was inspired by that of a super-Einstein manifold introduced earlier by A. Gray and T. J. Willmore in the context of mean-value theorems in Riemannian geometry. The dimension $4$ is the most interesting...

On real flag manifolds with cup-length equal to its dimension

Marko Radovanović (2020)

Czechoslovak Mathematical Journal

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We prove that for any positive integers $n_{1}, n_{2}, ..., n_{k}$ there exists a real flag manifold $F (1, ..., 1, n_{1}, n_{2}, ..., n_{k})$ with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.

Conformal Ricci Soliton in Lorentzian $α$ -Sasakian Manifolds

Tamalika Dutta, Nirabhra Basu, Arindam BHATTACHARYYA (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian $α$ -Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian $α$ -Sasakian manifold admitting conformal Ricci soliton is $η$ -Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian $α$ -Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian...

Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions

Yaning Wang, Ximin Liu (2014)

Annales Polonici Mathematici

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We consider an almost Kenmotsu manifold $M^{2 n + 1}$ with the characteristic vector field ξ belonging to the (k,μ)’-nullity distribution and h’ ≠ 0 and we prove that $M^{2 n + 1}$ is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a flat n-dimensional manifold, provided that $M^{2 n + 1}$ is ξ-Riemannian-semisymmetric. Moreover, if $M^{2 n + 1}$ is a ξ-Riemannian-semisymmetric almost Kenmotsu manifold such that ξ belongs to the (k,μ)-nullity distribution, we prove...

A contact metric manifold satisfying a certain curvature condition

Jong Taek Cho (1995)

Archivum Mathematicum

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In the present paper we investigate a contact metric manifold satisfying (C) $({\bar{\nabla}}_{\dot{γ}} R) (\cdot, \dot{γ}) \dot{γ} = 0$ for any $\bar{\nabla}$ -geodesic $γ$ , where $\bar{\nabla}$ is the Tanaka connection. We classify the 3-dimensional contact metric manifolds satisfying (C) for any $\bar{\nabla}$ -geodesic $γ$ . Also, we prove a structure theorem for a contact metric manifold with $ξ$ belonging to the $k$ -nullity distribution and satisfying (C) for any $\bar{\nabla}$ -geodesic $γ$ .

Displaying similar documents to “Some Properties of Lorentzian α -Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection”

Displaying similar documents to “Some Properties of Lorentzian $α$ -Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection”