On generalized Douglas-Weyl Randers metrics

Tayebeh Tabatabaeifar; Behzad Najafi; Mehdi Rafie-Rad

Displaying similar documents to “On generalized Douglas-Weyl Randers metrics”

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...

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.

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.

Three dimensional near-horizon metrics that are Einstein-Weyl

Matthew Randall (2017)

Archivum Mathematicum

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We investigate which three dimensional near-horizon metrics $g_{N H}$ admit a compatible 1-form $X$ such that $(X, [g_{N H}])$ defines an Einstein-Weyl structure. We find explicit examples and see that some of the solutions give rise to Einstein-Weyl structures of dispersionless KP type and dispersionless Hirota (aka hyperCR) type.

The discriminant and oscillation lengths for contact and Legendrian isotopies

Vincent Colin, Sheila Sandon (2015)

Journal of the European Mathematical Society

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We define an integer-valued non-degenerate bi-invariant metric (the discriminant metric) on the universal cover of the identity component of the contactomorphism group of any contact manifold. This metric has a very simple geometric definition, based on the notion of discriminant points of contactomorphisms. Using generating functions we prove that the discriminant metric is unbounded for the standard contact structures on $ℝ^{2 n} \times S^{1}$ and $ℝ P^{2 n + 1}$ . On the other hand we also show by elementary arguments...

Geodesically equivalent metrics on homogenous spaces

Neda Bokan, Tijana Šukilović, Srdjan Vukmirović (2019)

Czechoslovak Mathematical Journal

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Two metrics on a manifold are geodesically equivalent if the sets of their unparameterized geodesics coincide. We show that if two $G$ -invariant metrics of arbitrary signature on homogenous space $G / H$ are geodesically equivalent, they are affinely equivalent, i.e. they have the same Levi-Civita connection. We also prove that the existence of nonproportional, geodesically equivalent, $G$ -invariant metrics on homogenous space $G / H$ implies that their holonomy algebra cannot be full. We give an algorithm...

Semilinear equations, the $γ_{k}$ function, and generalized Gauduchon metrics

Jixiang Fu, Zhizhang Wang, Damin Wu (2013)

Journal of the European Mathematical Society

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In this paper, we generalize the Gauduchon metrics on a compact complex manifold and define the $γ_{k}$ functions on the space of its hermitian metrics.

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...

Pseudosymmetric and Weyl-pseudosymmetric $(κ, μ)$ -contact metric manifolds

N. Malekzadeh, E. Abedi, U.C. De (2016)

Archivum Mathematicum

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In this paper we classify pseudosymmetric and Ricci-pseudosymmetric $(κ, μ)$ -contact metric manifolds in the sense of Deszcz. Next we characterize Weyl-pseudosymmetric $(κ, μ)$ -contact metric manifolds.

The nonexistence of universal metric flows

Stefan Geschke (2018)

Commentationes Mathematicae Universitatis Carolinae

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We consider dynamical systems of the form $(X, f)$ where $X$ is a compact metric space and $f : X \to X$ is either a continuous map or a homeomorphism and provide a new proof that there is no universal metric dynamical system of this kind. The same is true for metric minimal dynamical systems and for metric abstract $ω$ -limit sets, answering a question by Will Brian.

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...

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.