Pradip Majhi

Bio: Pradip Majhi is an academic researcher from University of Calcutta. The author has contributed to research in topics: Manifold & Riemann curvature tensor. The author has an hindex of 5, co-authored 44 publications receiving 108 citations. Previous affiliations of Pradip Majhi include University of North Bengal.

Almost Kenmotsu metric as a conformal Ricci soliton

Abstract:

In the present paper, we characterize ( k , μ ) ′ (k,\mu )’ and generalized ( k , μ ) ′ (k,\mu )’ -almost Kenmotsu manifolds admitting the conformal Ricci soliton. It is also shown that a ( k , μ ) ′ (k,\mu )’ -almost Kenmotsu manifold M 2 n + 1 M^{2n+1} does not admit conformal gradient Ricci soliton ( g , V , λ ) (g,V,\lambda ) with V V collinear with the characteristic vector field ξ \xi . Finally an illustrative example is presented.

On invariant submanifolds of Kenmotsu manifolds

Abstract: The object of the present paper is to obtain a necessary condition for a three dimensional invariant submanifold of a Kenmotsu manifold to be totally geodesic. Besides this we study an invariant submanifold of Kenmotsu manifolds satisfying Q(α, R) = 0 and Q(S, α) = 0, where S, R are the Ricci tensor and curvature tensor respectively and α is the second fundamental form. Finally, we construct an example to verify our results.

Classifications of N(k)-contact metric manifolds satisfying certain curvature conditions

Abstract: The object of the present paper is to classify $N(k)$-contact metric manifolds satisfying certain curvature conditions on the projective curvature tensor. Projectively pseudosymmetric and pseudoprojectively at $N(k)$-contact metric manifolds are considered. Beside these we also study $N(k)$-contact metric manifolds satisfying $\tilde(Z)\dot P = 0$, where \tilde(Z)$ and $P$ denote respectively the concircular and projective curvature tensor. Finally, we give an example of a $N(k)$-contact metric manifold.

On mixed quasi-Einstein spacetimes

Abstract: The object of the present paper is to study mixed quasi-Einstein spacetimes, briefly M(QE)4 spacetimes. First we prove that every Z Ricci pseudosymmetric M(QE)4 spacetimes is a Z Ricci semisymmetric spacetime. Then we study Z flat spacetimes. Also we consider Ricci symmetric M(QE)4 spacetimes and among others we prove that the local cosmological structure of a Ricci symmetric M(QE)4 perfect fluid spacetime can be identified as Petrov type I, D or O. We show that such a spacetime is the Robertson-Walker spacetime. Moreover we deal with mixed quasi-Einstein spacetimes with the associated generators U and V as concurrent vector fields. As a consequence we obtain some important theorems. Among others it is shown that a perfect fluid M(QE)4 spacetime of non zero scalar curvature with the basic vector field of spacetime as velocity vector field of the fluid is of Segré characteristic [(1, 1, 1), 1]. Also we prove that a M(QE)4 spacetime can not admit heat flux provided the smooth function b is not equal to the cosmological constant k. This means that such a spacetime describe a universe which has already attained thermal equilibrium. Finally, we construct a non-trivial Lorentzian metric of M(QE)4.

Characterizations of the Lorentzian manifolds admitting a type of semi-symmetric metric connection

Abstract: We set a type of semi-symmetric metric connection on the Lorentzian manifolds. It is proved that a Lorentzian manifold endowed with a semi-symmetric metric $$\rho $$ -connection is a GRW spacetime. We also characterize the Ricci semisymmetric Lorentzian manifold and study the solution of Eisenhart problem of finding the second order parallel (skew-)symmetric tensor on Lorentzian manifolds. Finally, we address physical interpretation of some geometric results of our paper.