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

Payel Karmakar

Displaying similar documents to “Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold”

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...

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 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 Uniqueness Theoremsfor Ricci Tensor

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

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold $M$ and a symmetric 2-tensor $r$ , construct a metric on $M$ whose Ricci tensor equals $r$ . In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with...

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.

Vanishing conharmonic tensor of normal locally conformal almost cosymplectic manifold

Farah H. Al-Hussaini, Aligadzhi R. Rustanov, Habeeb M. Abood (2020)

Commentationes Mathematicae Universitatis Carolinae

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The main purpose of the present paper is to study the geometric properties of the conharmonic curvature tensor of normal locally conformal almost cosymplectic manifolds (normal LCAC-manifold). In particular, three conhoronic invariants are distinguished with regard to the vanishing conharmonic tensor. Subsequentaly, three classes of normal LCAC-manifolds are established. Moreover, it is proved that the manifolds of these classes are $η$ -Einstein manifolds of type $(α, β)$ . Furthermore, we have...

Almost invariant submanifolds for compact group actions

Alan Weinstein (2000)

Journal of the European Mathematical Society

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We define a $C^{1}$ distance between submanifolds of a riemannian manifold $M$ and show that, if a compact submanifold $N$ is not moved too much under the isometric action of a compact group $G$ , there is a $G$ -invariant submanifold $C^{1}$ -close to $N$ . The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds as zeros...

A Study on $φ$ -recurrence $τ$ -curvature tensor in $(k, μ)$ -contact metric manifolds

Gurupadavva Ingalahalli, C.S. Bagewadi (2018)

Communications in Mathematics

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In this paper we study $φ$ -recurrence $τ$ -curvature tensor in $(k, μ)$ -contact metric manifolds.

Global pinching theorems for minimal submanifolds in spheres

Kairen Cai (2003)

Colloquium Mathematicae

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Let M be a compact submanifold with parallel mean curvature vector embedded in the unit sphere $S^{n + p} (1)$ . By using the Sobolev inequalities of P. Li to get $L_{p}$ estimates for the norms of certain tensors related to the second fundamental form of M, we prove some rigidity theorems. Denote by H and ${| | σ | |}_{p}$ the mean curvature and the $L_{p}$ norm of the square length of the second fundamental form of M. We show that there is a constant C such that if ${| | σ | |}_{n / 2} < C$ , then M is a minimal submanifold in the sphere $S^{n + p - 1} (1 + H ²)$ with sectional...

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...