Kanak Kanti Baishya

Bio: Kanak Kanti Baishya is an academic researcher. The author has contributed to research in topics: Scalar curvature & Ricci curvature. The author has an hindex of 7, co-authored 23 publications receiving 168 citations.

On Concircular Structure Spacetimes

Abstract: This study presents a study of concircular structure spacetimes which are connected 4-dimensional Lorentzian concircular structure manifolds.

On Concircular Structure Spacetimes II

Abstract: We studied concircular structure spacetimes which are connected 4-dimensional Lorentzian concircular structure manifolds.

ON GENERALIZED QUASI-CONFORMAL N(k, μ)-MANIFOLDS

Abstract: . The object of the present paper is to introduce a new curva-ture tensor, named generalized quasi-conformal curvature tensor whichbridges conformal curvature tensor, concircular curvature tensor, pro-jective curvature tensor and conharmonic curvature tensor. Flatness andsymmetric properties of generalized quasi-conformal curvature tensor arestudied in the frame of (k,µ)-contact metric manifolds. 1. IntroductionIn 1968, Yano and Sawaki [27] introduced the notion of quasi-conformalcurvature tensor which contains both conformal curvature tensor as well asconcircular curvature tensor, in the context of Riemannian geometry. In tunewith Yano and Sawaki [27], the present paper attempts to introduce a newtensor field, named generalized quasi-conformal curvature tensor. The beautyof generalized quasi-conformal curvature tensor lies in the fact that it has theflavour of Riemann curvature tensor R, conformal curvature tensor C [8] con-harmonic curvature tensor Cˆ [9], concircular curvature tensor E [26, p. 84],projective curvature tensor P [26, p. 84] and m-projective curvature tensor H[15], as particular cases. The generalized quasi-conformal curvature tensor isdefined asW(X,Y)Z =2n−12n+1[(1−b+2na)−{1+2n(a+b)}c]C(X,Y )Z+[1−b+2na]E(X,Y)Z +2 n (b−a) P(X,Y )Z+2 n−12 n+1(1.1) (c −1){1+2 n(a +b)} Cˆ(X,Y)Zfor all X,Y,Z ∈ χ(M), the set of all vector field of the manifold M, where a,b and c are real constants. The above mentioned curvature tensors are defined

On D-homothetic deformation of trans-Sasakian structure

Abstract: Abs t rac t . The object of the present paper is to study a transformation called Dhomothetic deformation of trans-Sasakian structure. Among others it is shown that in a trans-Sasakian manifold, the Ricci operator Q does not commute with the structure tensor and the operator Q(j> — Q is conformal under a D-homothetic deformation. Also the (^-sectional curvature of a trans-Sasakian manifold is conformal under such a deformation. Some non-trivial examples of trans-Sasakian (non-Sasakian) manifolds with global vector fields are obtained.

On lorentzian quasi-einstein manifolds

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 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.

On pseudo quasi-Einstein manifolds

Abstract: The object of the present paper is to introduce a type of non-flat semi-Riemannian manifold, called pseudo quasi-Einstein manifold and to study some geometric and global properties of such a manifold. Also the existence of such a manifold is ensured by several non-trivial examples.

On Concircular Structure Spacetimes II

Abstract: We studied concircular structure spacetimes which are connected 4-dimensional Lorentzian concircular structure manifolds.

Slant and pseudo-slant submanifolds in LCS-manifolds

Abstract: We show new results on when a pseudo-slant submanifold is a LCS-manifold. Necessary and sufficient conditions for a submanifold to be pseudo-slant are given. We obtain necessary and sufficient conditions for the integrability of distributions which are involved in the definition of the pseudo-slant submanifold. We characterize the pseudoslant product and give necessary and sufficient conditions for a pseudo-slant submanifold to be the pseudo-slant product. Also we give an example of a slant submanifold in an LCS-manifold to illustrate the subject.