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On Generalized Ricci Recurrent Spacetimes
Chiranjib Dey 경북대학교 자연과학대학 수학과 2020 Kyungpook mathematical journal Vol.60 No.3
The object of the present paper is to characterize generalized Ricci recurrent (GR4) spacetimes. Among others things, it is proved that a conformally flat GR4 spacetime is a perfect fluid spacetime. We also prove that a GR4 spacetime with a Codazzi type Ricci tensor is a generalized Robertson Walker spacetime with Einstein fiber. We further show that in a GR4 spacetime with constant scalar curvature the energy momentum tensor is semisymmetric. Further, we obtain several corollaries. Finally, we cite some examples which are sufficient to demonstrate that the GR4 spacetime is non-empty and a GR4 spacetime is not a trivial case.
LORENTZIAN MANIFOLDS: A CHARACTERIZATION WITH SEMICONFORMAL CURVATURE TENSOR
De, Uday Chand,Dey, Chiranjib Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.3
In this paper we characterize semiconformally flat spacetimes and a spacetime with harmonic semiconformal curvature tensor. At first in a semiconformally flat perfect fluid spacetime we obtain a state equation and prove that in particular for dimension n = 4, the spacetime represents a model for incoherent radiation. Next we prove that perfect fluid spacetime with harmonic semiconformal curvature tensor is of Petrov type I, D or O and the spacetime is a GRW spacetime. As a consequence we obtain several corollaries.
The Critical Point Equation on 3-dimensional α-cosymplectic Manifolds
Blaga, Adara M.,Dey, Chiranjib Department of Mathematics 2020 Kyungpook mathematical journal Vol.60 No.1
The object of the present paper is to study the critical point equation (CPE) on 3-dimensional α-cosymplectic manifolds. We prove that if a 3-dimensional connected α-cosymplectic manifold satisfies the Miao-Tam critical point equation, then the manifold is of constant sectional curvature -α<sup>2</sup>, provided Dλ ≠ (ξλ)ξ. We also give several interesting corollaries of the main result.