• Title, Summary, Keyword: quasi Einstein

Search Result 29, Processing Time 0.031 seconds

ON A CLASS OF N(κ)-QUASI EINSTEIN MANIFOLDS

  • De, Avik;De, Uday Chand;Gazi, Abul Kalam
    • Communications of the Korean Mathematical Society
    • /
    • v.26 no.4
    • /
    • pp.623-634
    • /
    • 2011
  • The object of the present paper is to study N(${\kappa}$)-quasi Einstein manifolds. Existence of N(${\kappa}$)-quasi Einstein manifolds are proved. Physical example of N(${\kappa}$)-quasi Einstein manifold is also given. Finally, Weyl-semisymmetric N(${\kappa}$)-quasi Einstein manifolds have been considered.

𝒵 Tensor on N(k)-Quasi-Einstein Manifolds

  • Mallick, Sahanous;De, Uday Chand
    • Kyungpook Mathematical Journal
    • /
    • v.56 no.3
    • /
    • pp.979-991
    • /
    • 2016
  • The object of the present paper is to study N(k)-quasi-Einstein manifolds. We study an N(k)-quasi-Einstein manifold satisfying the curvature conditions $R({\xi},X){\cdot}Z=0$, $Z(X,{\xi}){\cdot}R=0$, and $P({\xi},X){\cdot}Z=0$, where R, P and Z denote the Riemannian curvature tensor, the projective curvature tensor and Z tensor respectively. Next we prove that the curvature condition $C{\cdot}Z=0$ holds in an N(k)-quasi-Einstein manifold, where C is the conformal curvature tensor. We also study Z-recurrent N(k)-quasi-Einstein manifolds. Finally, we construct an example of an N(k)-quasi-Einstein manifold and mention some physical examples.

ON LORENTZIAN QUASI-EINSTEIN MANIFOLDS

  • Shaikh, Absos Ali;Kim, Young-Ho;Hui, Shyamal Kumar
    • Journal of the Korean Mathematical Society
    • /
    • v.48 no.4
    • /
    • pp.669-689
    • /
    • 2011
  • 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 Robertson-Walker 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.

Super Quasi-Einstein Manifolds with Applications to General Relativity

  • Mallick, Sahanous
    • Kyungpook Mathematical Journal
    • /
    • v.58 no.2
    • /
    • pp.361-375
    • /
    • 2018
  • The object of the present paper is to study super quasi-Einstein manifolds. Some geometric properties of super quasi-Einstein manifolds have been studied. We also discuss $S(QE)_4$ spacetime with space-matter tensor and some properties related to it. Finally, we construct an example of a super quasi-Einstein spacetime.

Conformally Flat Quasi-Einstein Spaces

  • Chand De, Uday;Sengupta, Joydeep;Saha, Diptiman
    • Kyungpook Mathematical Journal
    • /
    • v.46 no.3
    • /
    • pp.417-423
    • /
    • 2006
  • The object of the present paper is to study a conformally flat quasi-Einstein space and its hypersurface.

  • PDF