Contact CR-warped Product Submanifolds Research Articles

Contact CR-Warped Product Submanifold of a Sasakian Space Form with a Semi-Symmetric Metric Connection

The main goal of this research paper is to investigate contact CR-warped product submanifolds within Sasakian space forms, utilizing a semi-symmetric metric connection. We conduct a comprehensive analysis of these submanifolds and establish several significant results. Additionally, we formulate an inequality that establishes a relationship between the squared norm of the second fundamental form and the warping function. Lastly, we present a number of geometric applications derived from our findings.

Ricci Curvature Inequalities for Contact CR-Warped Product Submanifolds of an Odd Dimensional Sphere Admitting a Semi-Symmetric Metric Connection

The primary objective of this paper is to explore contact CR-warped product submanifolds of Sasakian space forms equipped with a semi-symmetric metric connection. We thoroughly examine these submanifolds and establish various key findings. Furthermore, we derive an inequality relating the Ricci curvature to the mean curvature vector and warping function.

A Topological sphere theorem for contact CR-warped product submanifolds of an odd-dimensional unit sphere

AbstractIn this paper, we investigate topological sphere theorems for compact minimal contact CR-submanifolds of odd dimensional unit sphere. We show that if an inequality involving the warping function and the scalar curvature of the fibers is satisfied, a compact minimal contact CR-warped product submanifold of the odd dimensional unit sphere is homeomorphic to the sphere. In particular case, for 5-dimensional unit sphere, we show that a 4-dimensional compact minimal contact CR-warped product submanifold is homeomorphic to a sphere if ∣∇lnf∣2 < 1 is satisfied. By using Bonnet-Myers’s theorem we give a result about fundamental group and by Leung’s theorem we obtain a result about homology groups of a contact CR-warped submanifold.

Characterizing inequalities for existence of contact CR-warped product submanifolds of generalized Sasakian space forms admitting a nearly cosymplectic structure

This paper studies the contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly cosymplectic structure. Some inequalities for the existence of these types of warped product submanifolds are established, the obtained inequalities generalize the results that have acquired in \cite{atceken14}. Moreover, we also estimate another inequality for the second fundamental form in the expressions of the warping function, this inequality also generalizes the inequalities that have obtained in \cite{ghefari19}. In addition, we also explore the equality cases.

Ricci curvature of contact CR-warped product submanifolds in generalized Sasakian space forms admitting a trans-Sasakian structure

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

Homology of warped product submanifolds in the unit sphere and its applications

In this work, several pinched conditions on the Laplacian and gradient of the warping function are found in consideration of warped product submanifolds structure that force to homology groups vanish with no stable currents. Also, it is proved that a warped product pointwise semi-slant submanifold [Formula: see text] that is compact and oriented in an odd-dimensional spheres [Formula: see text] and [Formula: see text], has no stable integral [Formula: see text]-currents and [Formula: see text]-currents, respectively, and their homology groups are null, provided squared norm of the gradient for warping function satisfies some extrinsic restrictions including the Laplacian of the warping function, pointwise slant functions in addition to dimension of fiber of warped product immersions. Moreover, under assumption of extrinsic condition on the warping function, it is show [Formula: see text] being homeomorphic to a standard sphere [Formula: see text] with [Formula: see text] and homotopic to a standard sphere [Formula: see text] with [Formula: see text]. Further, the same results are generalized for contact CR-warped product submanifolds of same ambient spaces.

Ricci curvature of contact CR-warped product submanifolds in generalized Sasakian space forms admitting nearly Sasakian structure

<abstract> <p>The objective of this paper is to achieve the inequality for Ricci curvature of a contact CR-warped product submanifold isometrically immersed in a generalized Sasakian space form admitting a nearly Sasakian structure in the expressions of the squared norm of mean curvature vector and warping function. In addition, the equality case is likewise discussed. Later, we proved that under a certain condition the base manifold $N_T^{n_1}$ is isometric to a $n_1$-dimensional sphere $S^{n_1}(\frac{\lambda_1}{n_1})$ with constant sectional curvature $\frac{\lambda_1}{n_1}.$</p> </abstract>

Contact CR-warped product submanifolds of generalized Sasakian space forms admitting Ricci soliton

The objective of this paper is to study contact CR-warped product submanifolds admitting Ricci soliton in the setting of generalized Sasakian space forms with a nearly trans-Sasakian structure. More precisely, we obtain some classifications for these warped product submanifolds by using Ricci curvature and Euler–Lagrange equation

Contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly Sasakian structure

Contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly Sasakian structure

Contact CR-Warped Product of Submanifolds of the Generalized Sasakian Space Forms Admitting a Nearly Trans-Sasakian Structure

In the present paper, we apply Hopf’s lemma to the contact CR-warped product submanifolds of generalized Sasakian space forms admitting nearly trans-Sasakian structure and establish a characterization inequality for the existence of these types of warped products. The indicated inequality generalizes the inequalities obtained in [M. Atceken, Bull. Iranian Math. Soc., 39, No. 3, 415–429 (2013), M. Atceken, Collect. Math., 62, No. 1, 17–26 (2011), and S. Sular and C. Ozgur, Turkish J. Math., 36, 485–497 (2012)]. Moreover, we also deduce another inequality for the squared norm of the second fundamental form in terms of warping functions. This inequality is a generalization of the inequalities obtained in [I. Mihai, Geom. Dedicata, 109, 165–173 (2004) and K. Arslan, R. Ezentas, I. Mihai, and C. Murathan, J. Korean Math. Soc., 42, No. 5, 1101–1110 (2005)]. The inequalities deduced in the paper either generalize or improve all inequalities available in the literature and related to the squared norm of the second fundamental form for the contact CR-warped product submanifolds of any almost contact metric manifold.

Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications

It is known from [K. Yano and M. Kon, Structures on Manifolds (World Scientific, 1984)] that the integration of the Laplacian of a smooth function defined on a compact orientable Riemannian manifold without boundary vanishes with respect to the volume element. In this paper, we find out the some potential applications of this notion, and study the concept of warped product pointwise semi-slant submanifolds in cosymplectic manifolds as a generalization of contact CR-warped product submanifolds. Then, we prove the existence of warped product pointwise semi-slant submanifolds by their characterizations, and give an example supporting to this idea. Further, we obtain an interesting inequality in terms of the second fundamental form and the scalar curvature using Gauss equation and then, derive some applications of it with considering the equality case. We provide many trivial results for the warped product pointwise semi-slant submanifolds in cosymplectic space forms in various mathematical and physical terms such as Hessian, Hamiltonian and kinetic energy, and generalize the triviality results for contact CR-warped products as well.

Contact CR-Warped product Submanifolds in Cosymplectic Manifolds

Contact CR-Warped product Submanifolds in Cosymplectic Manifolds

Contact CR-Warped Product Submanifolds in Sasakian Space Forms

In this paper we consider Contact CR-warped product submanifolds and we investigate the status of equality in the inequality which has been found by I. Hasegawa and I. Mihai in [8]. 2000 AMS Classification: 53C25, 53C40

On contact CR-warped product submanifolds of a quasi-Sasakian manifold

On contact CR-warped product submanifolds of a quasi-Sasakian manifold

An inequality for contact CR-warped product submanifolds of nearly cosymplectic manifolds

Recently, Chen (Monatshefte Math. 133:177-195, 2001) established general sharp inequalities for CR-warped products in a Kaehler manifold. Afterward, Mihai obtained (Geom. Dedic. 109:165-173, 2004) the same inequalities for contact CR-warped product submanifolds of Sasakian space forms and derived some applications. In this paper, we obtain an inequality for the length of the second fundamental form of the warped product submanifold of a nearly cosymplectic manifold in terms of the warping function. The equality case is also discussed.MSC:53C40, 53C42, 53B25.

Contact CR-warped product submanifolds in generalized Sasakian space forms

We consider a contact CR-warped product submanifold M=M_{\top} \times_fM_{\bot} of a trans-Sasakian generalized Sasakian space form \widetilde{M} (f_1,f_2,f_3). We show that M is a contact CR-product under certain conditions.

A note on warped product submanifolds of Kenmotsu manifolds

Abstract Warped product manifolds are known to have applications in Physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star (cf. [HONG, S. T.: Warped products and black holes, Nuovo Cimento Soc. Ital. Fis. B 120 (2005), 1227–1234]). The studies on warped product manifolds with extrinsic geometric point of view are intensified after B. Y. Chen’s work on CR-warped product submanifolds of Kaehler manifolds. Later on, similar studies are carried out in the setting of Sasakian manifolds by Hasegawa and Mihai. As Kenmotsu manifolds are themselves warped product spaces, it is interesting to investigate warped product submanifolds of Kenmotsu manifolds. In the present note a larger class of warped product submanifolds than the class of contact CR-warped product submanifolds is considered. More precisely the existence of warped product submanifolds of a Kenmotsu manifold with one of the factors an invariant submanifold is ensured, an example of such submanifolds is provided and a characterization for a contact CR-submanifold to be a contact CR-warped product submanifold is established.

Contact CR-warped product submanifolds in cosymplectic space forms

The aim of this paper is to study the contact CR-warped product submanifolds in a cosymplectic space form and we obtain a necessary and sufficient condition for a contact CR-warped product submanifold to be a contact CR-product and give some new results.

Warped product contact CR-submanifolds of trans-Sasakian manifolds

B.Y. Chen [4] showed that there exists no proper warped CR-submanifolds N_ x ? NT of a Kaehler manifold and obtained many results on CR-warped products NT x ? N_. Contact CR-warped product submanifolds in Sasakian manifold were studied by I. Hasegawa and I. Mihai [6]. In this paper we have investigated the existence of contact CR-warped product submanifolds in more general setting of trans-Sasakian manifolds. .

Contact CR-Warped Product Submanifolds in Sasakian Space Forms

Recently, B.-Y. Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. Afterwards, I. Hasegawa and the present author obtained a sharp inequality for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Sasakian manifolds. In this paper, we improve the above inequality for contact CR-warped products in Sasakian space forms. Some applications are derived. A classification of contact CR-warped products in spheres, which satisfy the equality case, identically, is given.