This study attempts to establish new upper bounds on the mean curvature and constant sectional of first positive eigenvalue ψ − Laplacian operator Riemannian manifolds. Various approaches are being used find for closed oriented bi-slant submanifolds in a Sasakian space form. We extend different Reilly-like inequalities unit sphere depending our results operator. The conclusion this considers so...

We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.

In this paper, we consider Lorentz generalized Sasakian space forms admitting almost $\eta-$Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of \ soliton have introduced according to the choice special tensors such as Riemann, concircular, projective, $\mathcal{M-}$projective, $W_{1}$ and $W_{2}.$ Then, again tensor, necessary conditions are given for form be semisymmetri...

We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.

We propose a new method to construct degenerate $3$-$(\alpha,\delta)$-Sasakian manifolds as fiber products of Boothby-Wang bundles over hyperk\"ahler manifolds. Subsequently, we study homogeneous $3$-$(\alpha, \delta)$-Sasakian and prove that no non-trivial compact examples exist well there is exactly one family nilpotent Lie groups with this geometry, the quaternionic Heisenberg groups.

In the present paper, we have studied curvature properties of Schouten-van Kampen connection on n-dimensional Para Sasakian manifold and obtained some new results. Also, projective tensor, concircular Nijenhuis tensor for Para-Sasakian with respect to connection.

We classify locally homogeneous quasi-Sasakian manifolds in dimension five that admit a parallel spinor ψ of algebraic type F · ψ = 0 with respect to the unique connection ∇ preserving the quasi-Sasakian structure and with totally skew-symmetric torsion. We introduce a certain conformal transformation of almost contact metric manifolds and discuss a link between them and the dilation function i...