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

Sahanous Mallick; Uday Chand De

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$N (k)$ -quasi Einstein manifolds satisfying certain curvature conditions

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Rigidity of Einstein manifolds and generalized quasi-Einstein manifolds

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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.

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We consider generalized m-quasi-Einstein metric within the framework of Sasakian and K-contact manifolds. First, we prove that a complete Sasakian manifold M admitting a generalized m-quasi-Einstein metric is compact and isometric to the unit sphere $S^{2 n + 1}$ . Next, we generalize this to complete K-contact manifolds with m ≠ 1.

On the existence of generalized quasi-Einstein manifolds

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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.

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Characterization on Mixed Generalized Quasi-Einstein Manifold

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Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In the present paper we study characterizations of odd and even dimensional mixed generalized quasi-Einstein manifold. Next we prove that a mixed generalized quasi-Einstein manifold is a generalized quasi-Einstein manifold under a certain condition. Then we obtain three and four dimensional examples of mixed generalized quasi-Einstein manifold to ensure the existence of such manifold. Finally we establish the examples of warped product on mixed generalized quasi-Einstein manifold. ...

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Smooth metric measure spaces, quasi-Einstein metrics, and tractors

Jeffrey Case (2012)

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We introduce the tractor formalism from conformal geometry to the study of smooth metric measure spaces. In particular, this gives rise to a correspondence between quasi-Einstein metrics and parallel sections of certain tractor bundles. We use this formulation to give a sharp upper bound on the dimension of the vector space of quasi-Einstein metrics, providing a different perspective on some recent results of He, Petersen and Wylie.

Quasi-lines and their degenerations

Laurent Bonavero, Andreas Höring (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this paper we study the structure of manifolds that contain a quasi-line and give some evidence towards the fact that the irreducible components of degenerations of the quasi-line should determine the Mori cone. We show that the minimality with respect to a quasi-line yields strong restrictions on fibre space structures of the manifold.