On a compact quaternionic contact (qc) manifold of dimension bigger than seven and satisfying a Lichnerowicz type lower bound estimate we show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value then, up to a homothety of the qc structure, the manifold is qc equivalent to the standard 3-Sasakian sphere. The same conclusion is shown to hold on a non-compa...

The objective of this paper is to achieve the inequality for Ricci curvature a contact CR-warped product submanifold isometrically immersed in generalized Sasakian space form admitting trans-Sasakian structure expressions squared norm mean vector and warping function. We provide numerous physical applications derived inequalities. Finally, we prove that under certain condition base manifold iso...

In the present study, we considered 3-dimensional generalized (κ, μ)-contact metric manifolds. We proved that a 3-dimensional generalized (κ, μ)-contact metric manifold is not locally φ-symmetric in the sense of Takahashi. However such a manifold is locally φ-symmetric provided that κ and μ are constants. Also it is shown that if a 3-dimensional generalized (κ, μ) -contact metric manifold is Ri...

This paper aims to present work on contact pseudo-slant submanifolds of Para-Sasakian manifold. The study includes the definitions and some results type 1, 2, 3 submanifolds.

For a $$2n+1$$ -dimensional compact Sasakian manifold, if $$n\ge 2$$ , we prove that the analytic germ of variety representations fundamental group at every semi-simple representation is quadratic. To this result, almost-formality de Rham complex manifold with values in flat vector bundle. By almost-formality, also vanishing theorem on cup product cohomology bundles over manifold.

We study a Killing spinor type equation on spin Riemannian flows. We prove integrability conditions and partially classify those Riemannian flows M carrying non-trivial solutions to that equation in case M is a local Riemannian product, a Sasakian manifold or 3-dimensional. Mathematics Subject Classification: 53C12, 53C27

In this paper, we construct a framed f -structure on the slit tangent space of a Rizza manifold. This induces on the indicatrix bundle an almost contact metric. We find the conditions under which this structure reduces to a contact or to a Sasakian structure. Finally we study these structures on Kählerian Finsler manifolds. M.S.C. 2010: 53B40, 53C60, 32Q60, 53C15.

The object of the present paper is to study semi-symmetric metric connection on a 3-dimensional trans-Sasakian manifold. We found necessary condition under which vector field manifold will be strict contact field. Then, we obtained extended generalized phi-recurrent with respect connection. Next, satises ~L.~ S = 0 studied.

We propose fundamental inequalities for contact pseudo-slant submanifolds of (ϵ)-para Sasakian space form employing generalized normalized δ-Casorati curvature. characterize which equality cases hold and illustrate the main result with some applications. Further, we have considered a certain type submanifold Ricci soliton after computing its scalar curvature, developed an inequality to find cor...