quasi-Sasakian Manifolds Research Articles

Geometry of sub - Riemannian manifolds equipped with a semimetric quarter - symmetric connection

On a sub-Riemannian manifold we introduce a semimetric quarter-symmetric connection by defining intrinsic metric connection and two structural endomorphisms preserving the distribution on a sub-Riemannian manifold. We find conditions ensuring the metric property of the introduced connection. We clarify the nature of the structural endomorphisms of semimetric connection consistent with a sub-Riemannian quasi-static structure defined on non-holonomic Kenmotsu manifold and on almost quasi-Sasakian manifold. We find conditions, under which the mentioned manifolds are Einstein manifolds with respect to the quarter-symmetric connection.

Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton

In this paper, we examine 3-dimensional quasi-Sasakian manifold admitting conformal Ricci soliton. We give some theorems for $W_{0}^{*}$ flat, $\xi-W_{0}^{*}$ flat and $\phi-W_{0}^{*}$ semisymmetric 3-dimensional quasi-Sasakian manifold admitting conformal Ricci soliton. Also we study conformal Ricci soliton on a 3-dimensional quasi-Sasakian manifold satisfying the conditions $W_{0}^{*}(\xi,X).S=0$ and $R(\xi,X).W_{0}^{*}=0$.

Geometry of almost $3$-quasi-Sasakian manifolds of the second kind

Geometry of almost $3$-quasi-Sasakian manifolds of the second kind

Some results on the geometry of warped product CR-submanifolds in quasi-Sasakian manifold

Some results on the geometry of warped product CR-submanifolds in quasi-Sasakian manifold

The Schouten-van Kampen connection on quasi-Sasakian manifolds

"In the present paper, we study three-dimensional quasi-Sasakian manifolds admitting the Schouten-van Kampen connection. We characterize quasi-Sasakian manifolds and nd certain curvature properties with respect to the Schouten-van Kampen connection. Finally, we construct an example of a three-dimensional quasi-Sasakian manifold admitting the Schouten-van Kampen connection which veri es the results discussed in the present paper."

Riemann and Ricci bourguignon solitons on three-dimensional quasi-Sasakian manifolds

The aim of the present article is to analyze three-dimensional quasi-Sasakian manifolds admitting Riemann solitons and Ricci Bourguignon solitons.

$D_a$-HOMOTHETIC DEFORMATION AND RICCI SOLITIONS IN THREE DIMENSIONAL QUASI-SASAKIAN MANIFOLDS

In the present paper, we have studied curvature tensors of a quasi-Sasakian manifold with respect to the $D_a$-homothetic deformation. We have deduced the Ricci solition in quasi-Sasakian manifold with respect to the $D_a$-homothetic deformation. We have also proved that the quasi-Sasakian manifold is not $\bar{\xi}$-projectively flat under $D_a$-homothetic deformation. Also we give an example to prove the existance of quasi-Sasakian manifold.

Almost formality of quasi-Sasakian and Vaisman manifolds with applications to nilmanifolds

We provide models that are as close as possible to being formal for a large class of compact manifolds that admit a transversely Kaehler structure, including Vaisman and quasi-Sasakian manifolds. As an application we are able to classify the corresponding nilmanifolds.

Продолженные почти квазисасакиевы структуры

The notion of an almost quasi-Sasakian manifold is introduced. A ma­nifold with an almost quasi-Sasakian structure is a generalization of a quasi-Sasakian manifold; the difference is that an almost quasi-Sasakian manifold is almost normal. A characteristic criterion for an almost quasi-Sasakian manifold is formulated. Conditions are found under which al­most quasi-Sasakian manifolds are quasi-Sasakian manifolds. In particu­lar, an almost quasi-Sasakian manifold is a quasi-Sasakian manifold if and only if the first and second structure endomorphisms commute. An extended almost contact metric structure is defined on the distribution of an almost contact metric manifold. It follows from the definition of an extended structure that it is a quasi-Sasakian structure only if the original structure is cosymplectic with zero Schouten curvature tensor. It is proved that the constructed extended almost contact metric structure is the struc­ture of an almost quasi-Sasakian manifold if and only if the Schouten ten­sor of the original manifold is equal to zero. Relationships are found be­tween the second structure endomorphisms of the original and extended structures.

Submersions of Contact CR-Submanifolds of Generalized Quasi Sasakian Manifolds

In this paper, we discuss some properties of almost contact metric submersion of contact CR-submanifolds of generalized quasi-Sasakian manifold and derive some results based on their curvatures’s differential geometry. We also study de-Rham cohomology of CR-submanifold of generalized quasi-Sasakian manifold under the submersion.

On Pseudo-Slant Submanifolds of Nearly Quasi-Sasakian Manifolds

On Pseudo-Slant Submanifolds of Nearly Quasi-Sasakian Manifolds

Certain results for η-Ricci Solitons and Yamabe Solitons on quasi-Sasakian 3-Manifolds

We classify quasi-Sasakian 3-manifold with proper η-Ricci soliton and investigate its geometrical properties. Certain results of Yamabe soliton on such manifold are also presented. Finally, we construct an example of non-existence of proper η-Ricci soliton on 3-dimensional quasi-Sasakian manifold to illustrate the results obtained in previous section of the paper.

On Quasi-Sasakian Manifolds

In this paper we study three-dimensional quasi-Sasakian manifolds admitting the Schouten-van Kampen connection. Also, we study D-homothetic deformations on three-dimensional quasi-Sasakian manifolds admitting Schouten-van connection and projectively flat three-dimensional quasi-Sasakian manifolds admitting scv connection.

Warped Product Semi Slant Submanifold of Nearly Quasi Sasakian Manifold

Warped Product Semi Slant Submanifold of Nearly Quasi Sasakian Manifold

Ricci Almost Solitons on Three-Dimensional Quasi-Sasakian Manifolds

In this paper it is shown that a three-dimensional non-cosymplectic quasi-Sasakian manifold admitting Ricci almost soliton is locally $$\phi $$-symmetric. It is proved that a Ricci almost soliton on a three-dimensional quasi-Sasakian manifold reduces to a Ricci soliton. It is also proved that if a three-dimensional non-cosymplectic quasi-Sasakian manifold admits gradient Ricci soliton, then the potential function is invariant in the orthogonal distribution of the Reeb vector field $$\xi$$. We also improve some previous results regarding gradient Ricci soliton on three-dimensional quasi-Sasakian manifolds. An illustrative example is given to support the obtained results.

η-Ricci Solitons on Quasi-Sasakian Manifolds

Abstract The object of the present paper is to study η-Ricci solitons in a 3-dimensional non-cosymplectic quasi-Sasakian manifolds. We study a particular type of second order parallel tensor in this manifold. Beside this we consider this manifold satisfying some curvature properties of Ricci tensor.

Invariant and anti-invariant submanifolds of special quasi-sasakian manifolds

The present paper deals with the study of Chaki-pseudo parallel and Deszcz-pseudo parallel invariant submanifolds of SQ-Sasakian manifolds with respect to Levi–Civita connection as well as semisymmetric metric connection. It is obtained that these two classes are equivalent with a certain condition. In addition, invariant and anti-invariant submanifolds of SQ-Sasakian manifolds with respect to Levi–Civita connection as well as semisymmetric metric connection whose metrics are Ricci solitons are studied.

Skew semi-invariant submanifolds of generalized quasi-Sasakian manifolds

In the present paper, we study a new class of submanifolds of a generalized Quasi-Sasakian manifold, called skew semi-invariant submanifold. We obtain integrability conditions of the distributions on a skew semi-invariant submanifold and also find the condition for a skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold to be mixed totally geodesic. Also it is shown that a skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold will be anti-invariant if and only if $A_{\xi}=0$; and the submanifold will be skew semi-invariant submanifold if $\nabla w=0$. The equivalence relations for the skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold are given. Furthermore, we have proved that a skew semi-invariant $\xi^\perp$-submanifold of a normal almost contact metric manifold and a generalized Quasi-Sasakian manifold with non-trivial invariant distribution is $CR$-manifold. An example of dimension 5 is given to show that a skew semi-invariant $\xi^\perp$ submanifold is a $CR$-structure on the manifold.

Warped product pseudo-slant submanifolds of quasi-Sasakian manifolds

The object of the present paper is to study warped product and doubly warped product pseudo-slant submanifolds of quasi-Sasakian manifolds. We derive an example of proper pseudo-slant submanifold of almost contact metric manifold. Also, we study the non-existence of warped product and doubly warped product pseudo-slant submanifolds of quasi-Sasakian manifolds.

Magnetic curves in quasi-Sasakian 3-manifolds

We study magnetic trajectories corresponding to contact magnetic fields in 3-dimensional quasi-Sasakian manifolds. We show that they are slant curves, that is their contact angles are constant. We prove that such magnetic curves are geodesics for a certain linear connection for which all four structure tensor fields are parallel.