On exact 2-para Sasakian manifolds

Iordache, Mihai; Nicolescu, Liviu; Roşca, Radu

doi:10.1007/bf02857299

Cited by 35 publications

(53 citation statements)

References 6 publications

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“…In 1989 K. Matsumoto [26] introduced the notion of LPSasakian manifolds. Then I. Mihai and R. Rosca [28] introduced the same notion independently and later studied by many authors ( [27], [29], [40]). An n-dimensional smooth manifold M is said to be an LP-Sasakian manifold ( [6], [28]) if it admits an (1, 1) tensor field ϕ, a vector field ξ, an 1-form η and a Lorentzian metric g, which satisfy…”

Section: Some Examples Of Lqe Nmentioning

confidence: 99%

On Lorentzian Quasi-Einstein Manifolds

Shaikh¹,

Kim²,

Hui³

2011

Journal of the Korean Mathematical Society

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Abstract. The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the RobertsonWalker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study Lorentzian quasi-Einstein manifolds. Some basic geometric properties of such a manifold are obtained. The applications of Lorentzian quasi-Einstein manifolds to the general relativity and cosmology are investigated. Theories of gravitational collapse and models of Supernova explosions [5] are based on a relativistic fluid model for the star. In the theories of galaxy formation, relativistic fluid models have been used in order to describe the evolution of perturbations of the baryon and radiation components of the cosmic medium [32]. Theories of the structure and stability of neutron stars assume that the medium can be treated as a relativistic perfectly conducting magneto fluid. Theories of relativistic stars (which would be models for supermassive stars) are also based on relativistic fluid models. The problem of accretion onto a neutron star or a black hole is usually set in the framework of relativistic fluid models. Among others it is shown that a quasi-Einstein spacetime represents perfect fluid spacetime model in cosmology and consequently such a spacetime determines the final phase in the evolution of the universe. Finally the existence of such manifolds is ensured by several examples constructed from various well known geometric structures.

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Section: Some Examples Of Lqe Nmentioning

confidence: 99%

On Lorentzian Quasi-Einstein Manifolds

Shaikh¹,

Kim²,

Hui³

2011

Journal of the Korean Mathematical Society

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“…Then, Mihai and Roşca 2 introduced the same notion independently and they obtained several results on this manifold. LP-Sasakian manifolds have also been studied by Matsumoto and Mihai 3 , Mihai et al 4 , and Venkatesha and Bagewadi 5 .…”

Section: Introductionmentioning

confidence: 96%

Some Results on Lorentzian Para-Sasakian Manifolds

2011

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“…Then Mihai and Rosca [8] introduced the same notion and obtained several results in this manifold. Submanifolds of a Lorentzian almost paracontact manifold have been studied by Prasad and Ojha and defined a class of Lorentzian almost paracontact manifold as an LP-cosymplectic manifold in [9].…”

Section: Introductionmentioning

confidence: 96%