In this paper we introduce the concept of (Îµ)-almost paracontact manifolds, and in particular, of (Îµ)-para Sasakian manifolds. Several examples are presented. Some typical identities for curvatureâ€¦ (More)

In a Riemannian manifold, the existence of a new connection is proved. In particular cases, this connection reduces to several symmetric, semi-symmetric and quarter-symmetric connections; even someâ€¦ (More)

In N(k)-contact metric manifolds and/or (k, Î¼)-manifolds, gradient Ricci solitons, compact Ricci solitons and Ricci solitons with V pointwise collinear with the structure vector field Î¾ are studied.â€¦ (More)

We obtain a basic inequality involving the Laplacian of the warping function and the squared mean curvature of any warped product isometrically immersed in a Riemannian manifold (cf. Theorem 2.2).â€¦ (More)

We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, Î¸-slant, invariant andâ€¦ (More)

Generalized (Îº, Î¼)-space forms are introduced and studied. We deeply study the contact metric case and present examples for all possible dimensions. We also analyze the trans-Sasakian case. 2000â€¦ (More)

It is proved that a Riemannian manifold M isometrically immersed in a Sasakian space formËœM(c) of constant Ï•-sectional curvature c < 1, with the structure vector field Î¾ tangent to M, satisfiesâ€¦ (More)

In 1923, Eisenhart 1 gave the condition for the existence of a second-order parallel symmetric tensor in a Riemannian manifold. In 1925, Levy 2 proved that a second-order parallel symmetricâ€¦ (More)

It is proved that for a non-Sasakian Î·-Einstein (Îº, Î¼)-manifold M the following three conditions are equivalent: (a) M is flat and 3-dimensional, (b) M is Ricci-semisymmetric, and (c) M isâ€¦ (More)