Displaying similar documents to “Generalized m-quasi-Einstein metric within the framework of Sasakian and K-contact manifolds”

On a Class of Generalized quasi-Einstein Manifolds with Applications to Relativity

Sahanous Mallick, Uday Chand De (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Quasi Einstein manifold is a simple and natural generalization of Einstein manifold. The object of the present paper is to study some properties of generalized quasi Einstein manifolds. We also discuss G ( Q E ) 4 with space-matter tensor and some properties related to it. Two non-trivial examples have been constructed to prove the existence of generalized quasi Einstein spacetimes.

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...

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) ( ∇ ¯ γ ˙ R ) ( · , γ ˙ ) γ ˙ = 0 for any ∇ ¯ -geodesic γ , where ∇ ¯ is the Tanaka connection. We classify the 3-dimensional contact metric manifolds satisfying (C) for any ∇ ¯ -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 ∇ ¯ -geodesic γ .

On the existence of generalized quasi-Einstein manifolds

Uday Chand De, Sahanous Mallick (2011)

Archivum Mathematicum

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The object of the present paper is to study a type of Riemannian manifold called generalized quasi-Einstein manifold. The existence of a generalized quasi-Einstein manifold have been proved by non-trivial examples.

Rigidity of Einstein manifolds and generalized quasi-Einstein manifolds

Yi Hua Deng, Li Ping Luo, Li Jun Zhou (2015)

Annales Polonici Mathematici

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We discuss the rigidity of Einstein manifolds and generalized quasi-Einstein manifolds. We improve a pinching condition used in a theorem on the rigidity of compact Einstein manifolds. Under an additional condition, we confirm a conjecture on the rigidity of compact Einstein manifolds. In addition, we prove that every closed generalized quasi-Einstein manifold is an Einstein manifold provided μ = -1/(n-2), λ ≤ 0 and β ≤ 0.