Conformal Ricci Soliton in Lorentzian $\alpha $-Sasakian Manifolds

Tamalika Dutta; Nirabhra Basu; Arindam BHATTACHARYYA

Displaying similar documents to “Conformal Ricci Soliton in Lorentzian $α$ -Sasakian Manifolds”

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...

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...

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.

A strong maximum principle for the Paneitz operator and a non-local flow for the $Q$ -curvature

Matthew J. Gursky, Andrea Malchiodi (2015)

Journal of the European Mathematical Society

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In this paper we consider Riemannian manifolds $(M^{n}, g)$ of dimension $n \geq 5$ , with semi-positive $Q$ -curvature and non-negative scalar curvature. Under these assumptions we prove (i) the Paneitz operator satisfies a strong maximum principle; (ii) the Paneitz operator is a positive operator; and (iii) its Green’s function is strictly positive. We then introduce a non-local flow whose stationary points are metrics of constant positive $Q$ -curvature. Modifying the test function construction of Esposito-Robert,...

Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability

Marco L. A. Velásquez, André F. A. Ramalho, Henrique F. de Lima, Márcio S. Santos, Arlandson M. S. Oliveira (2021)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we investigate the geometry of conformal Killing graphs in a Riemannian manifold ${\bar{M}}_{f}^{n + 1}$ endowed with a weight function $f$ and having a closed conformal Killing vector field $V$ with conformal factor $ψ_{V}$ , that is, graphs constructed through the flow generated by $V$ and which are defined over an integral leaf of the foliation $V^{⊥}$ orthogonal to $V$ . For such graphs, we establish some rigidity results under appropriate constraints on the $f$ -mean curvature. Afterwards, we obtain some stability...

Singer-Thorpe bases for special Einstein curvature tensors in dimension 4

Zdeněk Dušek (2015)

Czechoslovak Mathematical Journal

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Let $(M, g)$ be a 4-dimensional Einstein Riemannian manifold. At each point $p$ of $M$ , the tangent space admits a so-called Singer-Thorpe basis (ST basis) with respect to the curvature tensor $R$ at $p$ . In this basis, up to standard symmetries and antisymmetries, just $5$ components of the curvature tensor $R$ are nonzero. For the space of constant curvature, the group $O (4)$ acts as a transformation group between ST bases at $T_{p} M$ and for the so-called 2-stein curvature tensors, the group $Sp (1) \subset SO (4)$ acts as a transformation...

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...

Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures

Amalendu Ghosh (2016)

Mathematica Bohemica

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We prove that a connected Riemannian manifold admitting a pair of non-trivial Einstein-Weyl structures $(g, \pm ω)$ with constant scalar curvature is either Einstein, or the dual field of $ω$ is Killing. Next, let $(M^{n}, g)$ be a complete and connected Riemannian manifold of dimension at least $3$ admitting a pair of Einstein-Weyl structures $(g, \pm ω)$ . Then the Einstein-Weyl vector field $E$ (dual to the $1$ -form $ω$ ) generates an infinitesimal harmonic transformation if and only if $E$ is Killing.

Structure of second-order symmetric Lorentzian manifolds

Oihane F. Blanco, Miguel Sánchez, José M. Senovilla (2013)

Journal of the European Mathematical Society

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$𝑆𝑒𝑐𝑜𝑛𝑑 - 𝑜𝑟𝑑𝑒𝑟𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐𝐿𝑜𝑟𝑒𝑛𝑡𝑧𝑖𝑎𝑛𝑠𝑝𝑎𝑐𝑒𝑠$ , that is to say, Lorentzian manifolds with vanishing second derivative $\nabla \nabla R \equiv 0$ of the curvature tensor $R$ , are characterized by several geometric properties, and explicitly presented. Locally, they are a product $M = M_{1} \times M_{2}$ where each factor is uniquely determined as follows: $M_{2}$ is a Riemannian symmetric space and $M_{1}$ is either a constant-curvature Lorentzian space or a definite type of plane wave generalizing the Cahen–Wallach family. In the proper case (i.e., $\nabla R \neq 0$ at some point), the curvature...

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 $\bar{M}$ of quasi-constant curvature subject to the condition that the characteristic vector field $ζ$ of $\bar{M}$ is tangent to $M$ . First, we provide a new result for such a lightlike hypersurface. Next, we investigate such a lightlike hypersurface $M$ of $\bar{M}$ such that (1) the screen distribution $S (T M)$ is totally umbilical or (2) $M$ is screen conformal.

Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity

Erwann Aubry, Colin Guillarmou (2011)

Journal of the European Mathematical Society

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For odd-dimensional Poincaré–Einstein manifolds $(X^{n + 1}, g)$ , we study the set of harmonic $k$ -forms (for $k < n / 2$ ) which are $C^{m}$ (with $m \in ℕ$ ) on the conformal compactification $\bar{X}$ of $X$ . This set is infinite-dimensional for small $m$ but it becomes finite-dimensional if $m$ is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology $H^{k} (\bar{X}, \partial \bar{X})$ and the kernel of the Branson–Gover [3] differential operators $(L_{k}, G_{k})$ on the conformal infinity $(\partial \bar{X}, [h_{0}])$ . We also relate the set of $C^{n - 2 k + 1} (Λ^{k} (\bar{X}))$ forms in the kernel of $d + δ_{g}$ ...

$η$ -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.

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.

Displaying similar documents to “Conformal Ricci Soliton in Lorentzian α -Sasakian Manifolds”

Displaying similar documents to “Conformal Ricci Soliton in Lorentzian $α$ -Sasakian Manifolds”