Semi-slant Submanifolds Research Articles

On the geometry of semi-slant submanifolds of a conformal Kenmotsu manifold

Abstract The object of this paper is to conduct an in-depth examination of semi-slant submanifolds within the framework of a conformal Kenmotsu manifolds. Our investigation is centered around identifying and understanding the conditions that ensure the integrability of both invariant and slant distributions, which play a pivotal role in defining semi-slant submanifolds. Additionally, we prove some interesting results for semi-slant submanifolds with parallel canonical structures.

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

An optimized Chen first inequality for semi-slant submanifolds in Lorentz Kenmotsu space forms

In this paper, we present necessary and sufficient conditions for a Lorentz contact manifold to be a Lorentz Kenmotsu manifold. Moreover, we obtain the optimal Chen first inequality for semi-slant submanifolds in Lorentz Kenmotsu space forms. Furthermore, the equality case of Chen inequality has been discussed.

Characterizations of warped product pointwise semi-slant submanifolds of Sasakian manifold

A warped product submanifold, whose tangent bundle can be decomposed to two orthogonal distributions; invariant and pointwise slant, is called a warped product pointwise semi-slant submanifold. The objective of this paper is to classify warped product pointwise semi-slant submanifolds, isometrically immersed into a Sasakian manifold. Park [25] provided the (non)-existence of a warped product pointwise semi-slant submanifold in a Sasakian manifold such that the structure vector field is tangential to fibers. In contrast, we provide intriguing theorems on warped product pointwise semi-slant submanifolds in a Sasakian manifold in terms of the shape operator and tensor fields such that the structure vector field is tangential to a base manifold and each fiber is a pointwise slant submanifold.

Quasi hemi Slant Submanifolds of Lorentzian Concircular Structures

n this manuscript, we introduce and explore quasi hemi-slant submanifolds, extending the concepts of slant submanifolds, semi-slant submanifolds, and hemi-slant submanifolds within Lorentzian concircular structures- manifolds (LCS)n -manifolds. We establish necessary and sufficient conditions for the integrability of distributions relevant to defining quasi hemi-slant submanifolds within Lorentzian concircular structuresmanifolds or (LCS)n- manifolds. Additionally, we investigate the conditions under which quasi hemi-slant submanifolds of Lorentzian concircular structures can be totally geodesic and analyze the geometric properties of foliations determined by the associated distribution.

Warped Product Pointwise Semi-slant Submanifolds of Almost Contact Manifolds

B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. By using the notion of pointwise slant submanifolds, we investigate the geometry of pointwise semi-slant submanifolds and their warped products in Sasakian and cosymplectic manifolds. We prove that there exist no proper pointwise semi-slant warped product submanifold other than contact CR-warped products in Sasakian manifolds. We give non-trivial examples of such submanifolds in cosymplectic manifolds and obtain several fundamental results, including a characterization for warped product pointwise semi-slant submanifolds.

Semi-slant submanifolds in a locally conformal Kaehler space form

In this paper, we consider semi-slant submanifolds in a locally conformal Kaehler manifold and a locally conformal Kaehler space form. We give inequalities for the length of the second fundamental form and the mean curvature and, using Gauss and Codazzi equations, we get many useful results in locally conformal Kaehler space form.

Impact of Semi-Symmetric Metric Connection on Homology of Warped Product Pointwise Semi-Slant Submanifolds of an Odd-Dimensional Sphere

Our paper explores warped product pointwise semi-slant submanifolds with a semi-symmetric metric connection in an odd-dimensional sphere and uncovers fundamental results. We also demonstrate how our findings can be applied to the homology of these submanifolds. Notably, we prove that under a specific condition, there are no stable currents for these submanifolds. This work adds valuable insights into the stability and behavior of warped product pointwise semi-slant submanifolds and sets the foundation for further research in this field.

De Rham Cohomology and Semi-Slant Submanifolds in Metallic Riemannian Manifolds

De Rham Cohomology and Semi-Slant Submanifolds in Metallic Riemannian Manifolds

Geometry of Warped Product CR and Semi-Slant Submanifolds in Quasi-Para-Sasakian Manifolds

In the present paper we study the existence or non-existence of warped product semi-slant submanifolds in quasi-para-Sasakian manifolds and prove that there are no proper warped product semi-slant submanifolds in a quasi-para-Sasakian manifold such that totally geodesic and totally umbilical submanifolds of warped product are proper semi-slant and invariant (or anti-invariant), respectively.

Inequalities for the Class of Warped Product Submanifold of Para-Cosymplectic Manifolds

The aim of this paper is to study the warped product pointwise semislant submanifolds in the para-cosymplectic manifold with the semi-Riemannian metric. For which, firstly we provide the more generalized definition of pointwise slant submanifolds and related characterization results followed by the definition of pointwise slant distributions and pointwise semislant submanifolds. We also derive some results for different foliations on distribution, and lastly, we defined pointwise semislant warped product submanifold, given existence and nonexistence results, basic lemmas, theorems, and optimal inequalities for the ambient manifold.

New Obstructions to Warped Product Immersions in Complex Space Forms

In this paper, we obtain a geometric inequality for warped product pointwise semi-slant submanifolds of complex space forms endowed with a semi-symmetric metric connection and discuss the equality case of this inequality. We provide some applications concerning the minimality and compactness of such submanifolds.

Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms

This paper aims to establish new upper bounds for the first positive eigenvalue of the Φ-Laplacian operator on Riemannian manifolds in terms of mean curvature and constant sectional curvature. The first eigenvalue for the Φ-Laplacian operator on closed oriented m-dimensional semislant submanifolds in a Sasakian space form is estimated in various ways. Several Reilly-like inequalities are generalized from our findings for Laplacian to the Φ-Laplacian on semislant submanifolds in a sphere with epsilon =1 and Phi =2.

Geometric Classification of Warped Products Isometrically Immersed into Conformal Sasakian Space Froms

Warped products play important roles in differential geometry, general relativity, and symmetry science. In this paper, we study the warped product pointwise semi-slant submanifolds that are isometrically immersed into conformal Sasakian space form. We show that there does not exist any proper warped product pointwise semi-slant submanifolds in conformal Sasakian manifolds. We derived some geometric inequalities for squared norm of second fundamental form from a warped product pointwise semi-slant submanifold into a conformal Sasakian manifolds.

Construction of Networks by Associating with Submanifolds of Almost Hermitian Manifolds

The idea that data lies in a non-linear space has brought up the concept of manifold learning as a part of machine learning and such notion is one of the most important research fields of today. The main idea here is to design the data as a submanifold model embedded in a high-dimensional manifold. On the other hand, graph theory is one of the most important research areas of applied mathematics and computer science. As a result, many researchers investigate new methods for machine learning on graphs. From the above information, it is seen that the theory of submanifolds and graph theory have become two important concepts in machine learning and nowadays, the geometric deep learning research area using these two concepts has emerged. By combining these two fields, this article aims to present the relationships between submanifolds of complex manifolds with the help of graphs. In this paper, we build some directed networks by identifying with submanifolds of almost Hermitian manifolds. Moreover, we give some results and relations among holomorphic submanifolds, totally real submanifolds, CR-submanifolds, slant submanifolds, semi-slant submanifolds, hemi-slant submanifolds, and bi-slant submanifolds in almost Hermitian manifolds in terms of graph theory.

Warped-twisted product semi-slant submanifolds

We introduce the notion of warped-twisted product semi-slant submanifolds of the form f2MT?f1 M? with warping function f2 on M? and twisting function f1, where MT is a holomorphic and M? is a slant submanifold of a globally conformal Kaehler manifold. We prove that a warped-twisted product semislant submanifold of a globally conformal Kaehler manifold is a locally doubly warped product. Then we establish a general inequality for doubly warped product semi-slant submanifolds and get some results for such submanifolds by using the equality sign of the general inequality.

A note on pointwise semi-slant submanifold of para-Cosymplectic manifolds

This article covers the geometric study of pointwise slant and pointwise semi-slant submanifolds of a para-Cosymplectic manifold M? 2m+1 with the semi-Riemannian metric. We give an advanced definition of these type of submanifolds for the spacelike and timelike vector fields. We obtain the characterization results for the involutive and totally geodesic foliation for such type of manifold M? 2m+1.

On the Topology of Warped Product Pointwise Semi-Slant Submanifolds with Positive Curvature

In this paper, we obtain some topological characterizations for the warping function of a warped product pointwise semi-slant submanifold of the form Ωn=NTl×fNϕk in a complex projective space CP2m(4). Additionally, we will find certain restrictions on the warping function f, Dirichlet energy function E(f), and first non-zero eigenvalue λ1 to prove that stable l-currents do not exist and also that the homology groups have vanished in Ωn. As an application of the non-existence of the stable currents in Ωn, we show that the fundamental group π1(Ωn) is trivial and Ωn is simply connected under the same extrinsic conditions. Further, some similar conclusions are provided for CR-warped product submanifolds.

Geometric Mechanics on Warped Product Semi-Slant Submanifold of Generalized Complex Space Forms

In this study, we develop a general inequality for warped product semi-slant submanifolds of type M n = N T n 1 × f N ϑ n 2 in a nearly Kaehler manifold and generalized complex space forms using the Gauss equation instead of the Codazzi equation. There are several applications that can be developed from this. It is also described how to classify warped product semi-slant submanifolds that satisfy the equality cases of inequalities (determined using boundary conditions). Several results for connected, compact warped product semi-slant submanifolds of nearly Kaehler manifolds are obtained, and they are derived in the context of the Hamiltonian, Dirichlet energy function, gradient Ricci curvature, and nonzero eigenvalue of the Laplacian of the warping functions.

Warped Product Submanifolds in Locally Golden Riemannian Manifolds with a Slant Factor

In the present paper, we study some properties of warped product pointwise semi-slant and hemi-slant submanifolds in Golden Riemannian manifolds, and we construct examples in Euclidean spaces. Additionally, we study some properties of proper warped product pointwise semi-slant (and, respectively, hemi-slant) submanifolds in a locally Golden Riemannian manifold.