trans-Sasakian Manifold Research Articles

Integrability of nearly trans-Sasakian manifolds

The geometry of integrable nearly trans-Sasakian manifolds (NST-manifolds) is studied in this paper. In particular, we consider as NST-manifolds with an integrable structure, normal NST-manifolds, and NST-manifolds satisfying the condition N(2)=0. Local structure of such manifolds is also described. We give a classification of NST-manifolds of constant Φ-holomorphic sectional curvature, as well as satisfying the axiom of Φ-holomorphic planes. NST-manifolds with a completely integrable first fundamental distribution are discussed.

Semi-slant Submanifolds of Trans-Sasakian Manifolds

The purpose of the present paper is to study semi-slant submanifolds of a trans-Sasakian manifold. 2000 Mathematics Subject Classification. 53C40, 53B25

Solitonical Inequality on Submanifolds in Trans-Sasakian Manifolds Coupled with a Slant Factor

Solitonical Inequality on Submanifolds in Trans-Sasakian Manifolds Coupled with a Slant Factor

A Generalization of Magnetic Curves in Contact Metric Geometry

In this paper we study some curves of a trans-Sasakian manifold that generalize magnetic curves.

Some Chen Inequalities for Submanifolds in Trans-Sasakian Manifolds Admitting a Semi-Symmetric Non-Metric Connection

In the present article, we study submanifolds tangent to the Reeb vector field in trans-Sasakian manifolds. We prove Chen’s first inequality and the Chen–Ricci inequality, respectively, for such submanifolds in trans-Sasakian manifolds which admit a semi-symmetric non-metric connection. Moreover, a generalized Euler inequality for special contact slant submanifolds in trans-Sasakian manifolds endowed with a semi-symmetric non-metric connection is obtained.

Trans-Sasakian Manifolds with Pseudo Finsler Metric

We introduce some properties and results for trans-Sasakian structures on indefinite Finsler manifolds in this paper. These structures are established on the 〖(M^0)〗^h and 〖(M^0)〗^v vector subbundles where M is an (2n+1) dimensional C^∞ manifold, M^0 is a non-empty open submanifold of TM. F^* is the fundamental Finsler function and〖 F〗^(2n+1)= (M,M^0,F^*) is an indefinite Finsler manifold. Furthermore, we give some formulas for α-Sasakian and β-Kenmotsu Finsler manifolds with pseudo-Finsler metric.

Nearly trans-Sasakian manifolds of constant holomorphic sectional curvature

The geometry of nearly trans-Sasakian manifolds of constant holomorphic sectional curvature is studied in this paper. It is proved that a harmonic nearly trans-Sasakian Einstein manifold is a manifold of non-positive scalar curvature, and, in the case of zero scalar curvature, it is locally equivalent to the product of a Ricci-flat nearly Kählerian manifold and the real line. Expressions for the Riemannian curvature and Ricci tensors are obtained. We show that a harmonic nearly trans-Sasakian manifold is a space of a constant curvature k=−χ2 if and only if it is canonically concircular to the manifold Cn×R equipped with the canonical cosymplectic structure. It is also proved that there are no harmonic nearly trans-Sasakian manifolds of constant positive curvature. The full classification of harmonic nearly trans-Sasakian manifolds of constant Φ-holomorphic sectional curvature is given.

Optimal Inequalities on (α,β)-Type Almost Contact Manifold with the Schouten–Van Kampen Connection

In the current research, we develop optimal inequalities for submanifolds in trans-Sasakian manifolds or (α,β)-type almost contact manifolds endowed with the Schouten–Van Kampen connection (SVK-connection), including generalized normalized δ-Casorati Curvatures (δ-CC). We also discuss submanifolds on which the equality situations occur. Lastly, we provided an example derived from this research.

On the Geometry of the Riemannian Curvature Tensor of Nearly Trans-Sasakian Manifolds

This paper presents the results of fundamental research into the geometry of the Riemannian curvature tensor of nearly trans-Sasakian manifolds. The components of the Riemannian curvature tensor on the space of the associated G-structure are counted, and the components of the Ricci tensor are calculated. Some identities are obtained that are satisfied by the Riemannian curvature tensors and the Ricci tensor. A number of properties are proved that characterize nearly trans-Sasakian manifolds with a closed contact form. The structure of nearly trans-Sasakian manifolds with a closed contact form is obtained. Several classes are singled out in terms of second-order differential-geometric invariants, and their local structure is obtained. The k-nullity distribution of a nearly trans-Sasakian manifold is studied.

(m,ρ)-quasi-Einstein solitons on 3-dimensional trans-Sasakian manifolds and its applications in spacetimes

This paper characterizes [Formula: see text]-quasi-Einstein solitons on [Formula: see text]-dimensional trans-Sasakian manifolds. It has been shown that a closed [Formula: see text]-quasi-Einstein soliton on a [Formula: see text]-dimensional trans-Sasakian manifold is either cosymplectic or Einstein under certain restrictions. Moreover, we investigate [Formula: see text]-quasi-Einstein solitons with certain potential vector fields on [Formula: see text]-dimensional trans-Sasakian manifolds. As an application of this soliton, we also analyze super quasi-Einstein spacetimes whose metrics are associated with [Formula: see text]-quasi-Einstein solitons.

Geometry of Harmonic Nearly Trans-Sasakian Manifolds

This paper considers a class of nearly trans-Sasakian manifolds. The local structure of nearly trans-Sasakian structures with a closed contact form and a closed Lee form is obtained. It is proved that the class of nearly trans-Sasakian manifolds with a closed contact form and a closed Lee form coincides with the class of almost contact metric manifolds with a closed contact form locally conformal to the closely cosymplectic manifolds. A wide class of harmonic nearly trans-Sasakian manifolds has been identified (i.e., nearly trans-Sasakian manifolds with a harmonic contact form) and an exhaustive description of the manifolds of this class is obtained. Also, examples of harmonic nearly trans-Sasakian manifolds are given.

Another Class of CR-slant Warped Product Submanifolds in Nearly Trans-Sasakian Manifolds

In this paper, we study a CR-slant warped product submanifold of the type B × f Mθ, where Mθ is a slant and B is a CR-product submanifold in a nearly trans-Sasakian manifold. We obtain an inequality for the squared norm of the second fundamental form in two cases, depending on the structure vector field affiliation, in such warped products. The equality case is also considered.

Aspects of Submanifolds on (α, β)-Type Almost Contact Manifolds with Quasi-Hemi-Slant Factor

In this study, the authors focus on quasi-hemi-slant submanifolds (qhs-submanifolds) of (α,β)-type almost contact manifolds, also known as trans-Sasakian manifolds. Essentially, we give sufficient and necessary conditions for the integrability of distributions using the concept of quasi-hemi-slant submanifolds of trans-Sasakian manifolds. We also consider the geometry of foliations dictated by the distribution and the requirements for submanifolds of trans-Sasakian manifolds with quasi-hemi-slant factors to be totally geodesic. Lastly, we give an illustration of a submanifold with a quasi-hemi-slant factor and discuss its application to number theory.

Almost *-η-Ricci soliton on three-dimensional trans-Sasakian manifolds

In this paper, we characterize three-dimensional trans-Sasakian manifolds of type [Formula: see text] admitting *-[Formula: see text]-Ricci-solitons and gradient almost *-[Formula: see text]-Ricci-solitons. First, we prove that a trans-Sasakian three-manifold of type [Formula: see text] admitting a *-[Formula: see text]-Ricci soliton reduces to a [Formula: see text]-Kenmostu manifold, provided potential vector field [Formula: see text] is Jacobi along a geodesic of [Formula: see text]. Next, we show that the trans-Sasakian metric as a gradient almost *-[Formula: see text]-Ricci soliton is either flat [Formula: see text] *-[Formula: see text]-Einstein [Formula: see text] a [Formula: see text]-Kenmotsu manifold.

Critical point equation within the framework of various contact metric manifolds

The aim of the present paper is to study the critical point equation (shortly CPE) conjecture within the framework of various contact metric manifolds. First we establish that Kenmotsu manifold satisfying the CPE either becomes an Einstein manifold or the derivative of potential function along characteristic vector field satisfy a certain relation on the distribution of η. Next we study CPE on (κ, μ)'-almost Kenmotsu manifold and obtain that the manifold is Einstein. Later in case of 3-dimensional trans-Sasakian manifold, we get that either the manifold becomes α-Sasakian or it becomes Einstein. Finally we give examples of 3-dimensional trans-Sasakian manifold and (κ ,μ)'-almost Kenmotsu manifold to verify our outcomes.

Optimal Inequalities for Submanifolds in Trans-Sasakian Manifolds Endowed with a Semi-Symmetric Metric Connection

In this paper, we improve the Chen first inequality for special contact slant submanifolds and Legendrian submanifolds, respectively, in (α,β) trans-Sasakian generalized Sasakian space forms endowed with a semi-symmetric metric connection.

Geometry of CR-slant Warped Products in Nearly Trans-Sasakian Manifolds

A CR-slant warped product is considered a generalization of a CR-warped product. It was firstly introduced and studied in the field of Kaehler geometry. In this paper, we study CR-slant warped products in nearly trans-Sasakian manifolds. We obtain a general inequality related to the second fundamental form and the warping function in such warped products. The equality case is discussed.

Generalized Trans-Sasakian manifolds

In this paper, we study the class of almost contact metric manifolds which are conformal to Trans-Sasakian manifolds, and we construct concrete examples from almost Hermitian manifolds using the product of manifolds. As a consequence, we obtain several properties for the three-dimensional case.

On the geometry of nearly trans-Sasakian manifolds

The geometry of nearly trans-Sasakian manifolds is researched in this paper. The complete group of structural equations and the components of the Lee vector on the space of the associated $G$-structure are obtained for such manifolds. Conditions are found under which a nearly trans-Sasakian structure is a trans-Sasakian, a cosymplectic, a closely cosymplectic, a Sasakian structure or a Kenmotsu structure. The conditions are obtained when the nearly trans-Sasakian structure is a special generalized Kenmotsu structure of the second kind. A complete classification of nearly trans-Sasakian manifolds is obtained, i.e. it is proved that a nearly trans-Sasakian manifold is either a trans-Sasakian manifold or has a closed contact form. It is proved that the nearly trans-Sasakian structure with a nonclosed contact form is homothetic to the Sasakian structure. The criterion of ownership of a nearly trans-Sasakian structure is obtained. It is proved that the class of nearly trans-Sasakian manifolds with a closed contact form and a closed Lee form coincides with the class of almost contact metric manifolds with a closed contact form, which are locally conformal to the closely cosymplectic manifolds. Examples of such manifolds are given. The necessary and sufficient conditions for the complete integrability of the first fundamental distribution of a nearly trans-Sasakian manifold are obtained. It is proved that a nearly K\"ahler structure on the leaves of the first fundamental distribution of a nearly trans-Sasakian manifold is induced.

$\eta$-Ricci soliton in an indefinite Trans-Sasakian manifold admitting semi-symmetric metric connection

In this paper, we intend to study some of the curvature tensor of $\eta$-Ricci solitons of indefinite Trans-Sasakian manifold admitting semi-symmetric metric connection.