Sasakian Manifolds Research Articles

Riemann soliton within the framework of contact geometry

In this paper, we study contact metric manifold whose metric is a Riemann soliton. First, we consider Riemann soliton (g, V ) with V as contact vector field on a Sasakian manifold (M, g) and in this case we prove that M is either of constant curvature +1 (and V is Killing) or D-homothetically fixed η-Einstein manifold (and V leaves the structure tensor φ invariant). Next, we prove that if a compact K-contact manifold whose metric g is a gradient almost Riemann soliton, then it is Sasakian and isometric to a unit sphere S 2n+1. Further, we study H-contact manifold admitting a Riemann soliton (g, V ) where V is pointwise collinear with ξ.

Transverse Kähler–Ricci Solitons of Five-Dimensional Sasaki–Einstein Spaces Yp,q and T1,1

We investigate the deformations of the Sasaki–Einstein structures of the five-dimensional spaces T 1 , 1 and Y p , q by exploiting the transverse structure of the Sasaki manifolds. We consider local deformations of the Sasaki structures preserving the Reeb vector fields but modify the contact forms. In this class of deformations, we analyze the transverse Kähler–Ricci flow equations. We produce some particular explicit solutions representing families of new Sasakian structures.

η-Einstein Sasakian immersions in non-compact Sasakian space forms

The aim of this paper is to study Sasakian immersions of (non-compact) complete regular Sasakian manifolds into the Heisenberg group and into $$ {\mathbb{B}}^N\times {\mathbb{R}}$$ equipped with their standard Sasakian structures. We obtain a complete classification of such manifolds in the η-Einstein case.

Three dimensional Sasakian manifolds admitting η-Ricci solitons

Three dimensional Sasakian manifolds admitting η-Ricci solitons

Some properties of pseudo-slant submanifolds of a Sasakian manifold

Some properties of pseudo-slant submanifolds of a Sasakian manifold

Quasi hemi-slant submanifolds of Sasakian manifolds

In this paper, we define and study quasi hemi-slant submanifolds as a generalization of slant submanifolds, semi-slant submanifolds and hemi-slant submanifolds of contact metric manifolds [ In particular, for a Sasakian manifold]. Further, we obtain necessary and sufficient conditions for integrability of distributions which are involved in the definition of quasi hemi-slant submanifolds of Sasakian manifolds. After it, we investigate the necessary and sufficient condition for quasi hemi-slant submanifolds of Sasakian manifolds to be totally geodesic. Finally, we obtain the necessary and sufficient condition for a quasi hemi-slant submanifold to be local product Riemannian manifold and also give an example of such submanifolds.

Three dimensional Sasakian manifolds admitting η-Ricci solitons

In this paper we characterize the three dimensional Sasakian manifolds admitting η-almost Ricci solitons. After the introduction, in section 2, we study three dimensional Sasakian manifolds. In section 3, we prove that an η-Ricci soliton in Sasakian manifolds satisfying the curvature property R.Q = 0 is shrinking and reduces to Ricci soliton. In section 4, we show that the necessary and suficient condition for a Sasakian manifold not admitting a proper η-Ricci soliton is that it is Ricci symmetric. In sections 5 and 6, we study projectively at and concircularly at Sasakian manifold of dimension 3 respectively and find the type of an η-Ricci soliton on such manifold. The next section is devoted to the study of such a manifold admitting η-Ricci soliton and we prove some equivalent conditions. Finally, in section 8, we prove that in a three dimensional Sasakian manifold an η-Ricci soliton becomes Ricci soliton if and only if it is Ricci pseudo-symmetric.

* -Ricci solitons on ε-para sasakian 3-manifolds

In the present paper we study *-Ricci solitons in (Є)–para Sasakian manifolds and prove that if an (Є)-para Sasakian 3-manifold with constant scalar curvature admits a *-Ricci soliton, then the *-Ricci soliton is steady if and only if ℒVξ is g-orthogonal to ξ provided a =Trϕ is constant. Beside these, we study gradient *-Ricci solitons on (Є) –para Sasakian 3-manifolds.

Study on generalised pseudo (Ricci) symmetric Sasakian manifold admitting general connection

The object of the present paper is to study the generalized pseudo (Ricci) symmetric Sasakian manifold with respect to a new connection named general connection. The general connection has the flavor of the quarter-symmetric connection, generalized Tanaka-Webster connection, Zamkovoy, and Schouten- van Kampen connection. The existence of generalized pseudo (Ricci) symmetric Sasakian manifold with respect to general connection is ensured by an example.

Some properties of pseudo-slant submanifolds of a Sasakian manifold

In this paper, we study pseudo-slant submanifolds of a Sasakian manifold. We find some results and investigate the integrability conditions of distributions which are involved in the definition of pseudo-slant submanifolds. Finally, we obtain the necessary and sucifient condition for a pseudo-slant submanifold to be pseudo-slant product.

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.

Branched holomorphic Cartan geometry on Sasakian manifolds

We extend the notion of (branched) holomorphic Cartan geometry on a complex manifold to the context of Sasakian manifolds. Branched holomorphic Cartan geometries on Sasakian Calabi-Yau manifolds are investigated.

Some more results on Ɛ-LP-Sasakian manifolds admitting η –Ricci solutions

The object of the present paper is to characterize e − LP −Sasakian manifolds with a quarter-symmetric metric connection admitting η−Ricci solitons. Finally, the existence of η−Ricci soliton in an e − LP −Sasakian manifold has been proved by a concrete example.

Geometry of warped product pointwise submanifolds of Sasakian manifolds

Recently, Chen and Uddin introduced and studied warped product pointwise bi-slant submanifolds of K?hler manifolds in [13]. They have obtained many interesting results. In the present paper, we investigate warped product pointwise bi-slant submanifolds in Sasakian manifolds and we derive contact version of results obtain in [13]. We give a non-trivial example to prove the existence of these submanifolds.

Quasi hemi-slant submanifolds of Sasakian manifolds

Quasi hemi-slant submanifolds of Sasakian manifolds

Hemi-slant ξ⊥-Riemannian submersions in contact geometry

M. A. Akyol and R. Sar? [On semi-slant ??-Riemannian submersions, Mediterr. J. Math. 14(6) (2017) 234.] defined semi-slant ??-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. As a generalization of the above notion and natural generalization of anti-invariant ??-Riemannian submersions, semi-invariant ??-Riemannian submersions and slant submersions, we study hemi-slant ??-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We obtain the geometry of foliations, give some examples and find necessary and sufficient condition for the base manifold to be a locally product manifold. Moreover, we obtain some curvature relations from Sasakian space forms between the total space, the base space and the fibres.

Sasakian structures on products of real line and Kahlerian manifold

In this paper, we construct a Sasakian manifold by the product of real line and K\{a}hlerian manifold with exact K\{a}hler form. This result demonstrates the close relation between Sasakian and K\{a}hlerian manifold with exact K\{a}hler form. We present an example and an open problem.

Lightlike Hypersurfaces of an Indefinite Para Sasakian Manifold

In this paper, we initiate the study of lightlike hypersurfaces of an indefinite almost paracontact metric manifold which are tangent to the structure vector field. In particular, we give definitions of invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, and give some examples. Integrability conditions for the distributions involved in the screen semi-invariant lightlike hypersurface of an indefinite para Sasakian manifold are investigated.

Some Result on Contact Pseudo-Slant Submanifolds of a Sasakian Manifold

In this paper, we study the geometry of the contact pseudo-slant submanifolds of a Sasakian manifold. We derive the integrability conditions of distributions in the definition of a contact pseudo-slant submanifold. The notions contact pseudo-slant product is defined, and the necessary and sufficient conditions for a submanifold to contact pseudo-slant product is given. Also, a non-trivial example is used to demonstrate that the method presented in this paper is effective.

Einstein-Weyl structures on trans-Sasakian manifolds

AbstractIn this article we study Einstein-Weyl structures on a 3-dimensional trans-Sasakian manifoldMof type (α,β). First, we prove that a 3-dimensional trans-Sasakian manifold admitting both Einstein-Weyl structuresW±= (g, ±θ) is Einstein, or is homothetic to a Sasakian manifold ifα≠ 0. Next forβ≠ 0 it is proved thatMis Einstein, or is homothetic to anf-Kenmotsu manifold if it admits an Einstein-Weyl structureW= (g,κη) for some nonzero constantκ. Finally, a classification is obtained when a trans-Sasakian manifold admits a closed Einstein-Weyl structure. Further, ifMis compact we also obtain two corollaries.