Pradip Majhi

Abstract: The object of the present paper is to study ϕ -Weyl semisymmetric and ϕ -projectively semisymmetric generalized Sasakian space-forms. Finally, illustrative examples are given.

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.

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.

Abstract: The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting Ricci-Yamabe soliton. It is shown that a $(k,\mu)'$-almost Kenmotsu manifold admitting a Ricci-Yamabe soliton or gradient Ricci-Yamabe soliton is locally isometric to the Riemannian product $\mathbb{H}^{n+1}(-4) \times \mathbb{R}^n$. For the later case, the potential vector field is pointwise collinear with the Reeb vector field. Also, a $(k,\mu)$-almost Kenmotsu manifold admitting certain Ricci-Yamabe soliton with the curvature property $Q \cdot P = 0$ is locally isometric to the hyperbolic space $\mathbb{H}^{2n+1}(-1)$ and the non-existense of the curvature property $Q \cdot R = 0$ is proved.

Abstract: A Riemannian manifold (M,g) is called a quasi Einstein manifold if for any coordinate system in M, its Ricci tensor S satisfes S_(ij) = ag_(ij) + bA_iA_j for some scalars a and b, where A(X)=g(X, p) for some unit vector p. This class of manifolds is a generalization of Einstein manifolds which are quasi Einstein manifolds whose b=0. In this paper, we will give examples of these manifolds and we will show that on each coordinate system, a and b are unique.