Bi-slant Submanifolds Research Articles

On warped product pointwise quasi bi-slant submanifolds of Kenmotsu manifolds

On warped product pointwise quasi bi-slant submanifolds of Kenmotsu manifolds

A generalized Wintgen inequality in quaternion Kähler geometry

In this paper, we establish a generalized Wintgen inequality for quaternionic bi-slant submanifolds and QR-submanifolds (with minimal codimension) in quaternion space forms. We also aim to characterize the second fundamental form of those submanifolds for which the equality cases can hold. Finally, we provide examples of submanifolds embedded in quaternion space forms to support our results.

Pinching Results for Doubly Warped Products’ Pointwise Bi-Slant Submanifolds in Locally Conformal Almost Cosymplectic Manifolds with a Quarter-Symmetric Connection

In this research paper, we establish geometric inequalities that characterize the relationship between the squared mean curvature and the warping functions of a doubly warped product pointwise bi-slant submanifold. Our investigation takes place in the context of locally conformal almost cosymplectic manifolds, which are equipped with a quarter-symmetric metric connection. We also consider the cases of equality in these inequalities. Additionally, we derive some geometric applications of our obtained results.

Warped product pointwise bi-slant submanifolds of locally product Riemannian manifolds.

In this paper we introduce the concept of pointwise bi-slant
 submanifolds of locally product Riemannian manifolds and studied warped
 product pointwise bi-slant submanifolds of locally product Riemannian
 manifolds. We obtain some characterization results for warped products
 pointwise bi-slant submanifolds. Also, we provide some non-trivial
 examples of such warped product submanifolds.

Warped Product Quasi Bi-Slant Submanifolds of Kaehler Manifolds

Warped Product Quasi Bi-Slant Submanifolds of Kaehler Manifolds

Quasi Bi-slant Submanifolds of Locally Metallic Riemannian Manifolds

In this article, we investigate quasi bi-slant submanifolds of locally metallic Riemannian manifolds. The main objective is to determine the conditions under which the distributions used in defining these submanifolds are integrable. We also establish the necessary and sufficient conditions for quasi bi-slant submanifold to be a totally geodesic foliation.

Characterization of bi-slant submanifolds of paraSasakian manifold

This paper aims to present work on bi-slant submanifolds of paraSasakian manifold. The study includes the definitions and some results on Type 1, Type 2, and Type 3 slant submanifolds. We define bi-slant submanifolds and derive characterization results with some illustrative examples. Further, we also study the particular cases of bi-slant submanifolds named semi-slant and pseudo-slant submanifolds and derive some results. An example for each case is also constructed.

Pointwise bi-slant submanifolds of a Kenmotsu manifold

In the present paper, point wise bi-slant submanifolds are studied. Some geometrically important results are obtained in the second section and these findings are used in the third section to investigate bislant warped product submanifolds of a Kenmotsu manifold. In the last section of the paper, an inequality for the squared norm of the second fundamental form of a sequential warped product submanifold of a Kenmotsu manifold is established.

Bounds on Ricci curvature for doubly warped products pointwise bi-slant submanifolds and applications to physics

In this article, we obtain bounds for Ricci curvature for doubly warped products pointwise bi-slant submanifolds in generalized complex space forms and discuss the equality case of the inequality. We also derive the non-existence of such immersions. Finally, we construct some applications of the result in terms of the Harmonic function, Hessian tensor, and Dirchilet energy function.

Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms

In this article, we derive Chen’s inequalities involving Chen’s δ-invariant δM, Riemannian invariant δ(m1,⋯,mk), Ricci curvature, Riemannian invariant Θk(2≤k≤m), the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application of the obtain inequality, we first derived the Chen inequality for the bi-slant submanifold of generalized Sasakian-space-forms.

Estimation of Eigenvalues for the ψ-Laplace Operator on Bi-Slant Submanifolds of Sasakian Space Forms

This study attempts to establish new upper bounds on the mean curvature and constant sectional curvature of the first positive eigenvalue of the ψ − Laplacian operator on Riemannian manifolds. Various approaches are being used to find the first eigenvalue for the ψ − Laplacian operator on closed oriented bi-slant submanifolds in a Sasakian space form. We extend different Reilly-like inequalities to the ψ − Laplacian on bi-slant submanifolds in a unit sphere depending on our results for the Laplacian operator. The conclusion of this study considers some special cases as well.

Some Pinching Results for Bi-Slant Submanifolds in S-Space Forms

The objective of the present article is to prove two geometric inequalities for submanifolds in S-space forms. First, we establish inequalities for the generalized normalized δ-Casorati curvatures for bi-slant submanifolds in S-space forms and then we derive the generalized Wintgen inequality for Legendrian and bi-slant submanifolds in the same ambient space. We also discuss the equality cases of the inequalities. Further, we provide some immediate geometric applications of the results. Finally, we construct some examples of slant and Legendrian submanifolds, respectively.

Quasi Bi-Slant Submanifolds of Kaehler Manifolds

In this paper, we introduce the new notion of quasi bi-slant submanifolds of almost Hermitian manifolds. Necessary and sufficient conditions for the integrability of distributions which are involved in the definition of such submanifolds of a Kaehler manifold are obtained. We also investigate the necessary and sufficient conditions for these submanifolds of Kaehler manifolds to be totally geodesic and study the geometry of foliations determined by the above distributions. Finally, we obtain the necessary and sufficient conditions for a quasi bi-slant submanifold to be local product Riemannian manifold and also construct some examples of such submanifolds.

Generalized Wintgen inequality for BI-SLANT submanifolds in conformal Sasakian space form with quarter-symmetric connection

PurposeIn 1979, P. Wintgen obtained a basic relationship between the extrinsic normal curvature the intrinsic Gauss curvature, and squared mean curvature of any surface in a Euclidean 4-space with the equality holding if and only if the curvature ellipse is a circle. In 1999, P. J. De Smet, F. Dillen, L. Verstraelen and L. Vrancken gave a conjecture of Wintgen inequality, named as the DDVV-conjecture, for general Riemannian submanifolds in real space forms. Later on, this conjecture was proven to be true by Z. Lu and by Ge and Z. Tang independently. Since then, the study of Wintgen’s inequalities and Wintgen ideal submanifolds has attracted many researchers, and a lot of interesting results have been found during the last 15 years. The main purpose of this paper is to extend this conjecture of Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection.Design/methodology/approachThe authors used standard technique for obtaining generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection.FindingsThe authors establish the generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection, and also find conditions under which the equality holds. Some particular cases are also stated.Originality/valueThe research may be a challenge for new developments focused on new relationships in terms of various invariants, for different types of submanifolds in that ambient space with several connections.

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.

On pointwise quasi bi-slant submanifolds

In this paper, we introduce a new class of submanifolds which are called pointwise quasi bi-slant submanifolds in almost Hermitian manifolds which extends quasi bi-slant, bi-slant, hemi-slant, semi-slant and slant submanifolds in a very natural way. Several basic results in this respect are proved in this paper. Moreover, we obtain some conditions of the distributions which is involved in the definition of the new submanifolds. We also get some results for totally geodesic and mixed totally geodesic conditions for pointwise quasi bi-slant submanifolds. Finally, we illustrate some examples in order to guarantee the new kind of submanifolds.

A Study of Doubly Warped Product Immersions in a Nearly Trans-Sasakian Manifold with Slant Factor

In this article, we discuss the de Rham cohomology class for bislant submanifolds in nearly trans-Sasakian manifolds. Moreover, we give a classification of warped product bislant submanifolds in nearly trans-Sasakian manifolds with some nontrivial examples in the support. Next, it is of great interest to prove that there does not exist any doubly warped product bislant submanifolds other than warped product bislant submanifolds in nearly trans-Sasakian manifolds. Some immediate consequences are also obtained.

Bi-slant submanifolds of an S manifold

PurposeBi-slant submanifolds of S-manifolds are introduced, and some examples of these submanifolds are presented.Design/methodology/approachSome properties of Di-geodesic and Di-umbilical bi-slant submanifolds are examined.FindingsThe Riemannian curvature invariants of these submanifolds are computed, and some results are discussed with the help of these invariants.Originality/valueThe topic is original, and the manuscript has not been submitted to any other journal.

Some Results for Bislant and Semi-Slant Submanifolds of Semi-Riemannian Manifolds

This study looks into the bislant submanifolds of almost product semi-Riemannian manifolds that are Riemannian, semi-Riemannian and lightlike. We also state the theorems that provide the required conditions for constructing a slant submanifold from a bislant submanifold. Morever, we define the semi-slant submanifolds of locally product semi-Riemannian manifolds and discuss the integrability conditions of distributions that are invariants or slants that constitute a semi-slant submanifold.

Warped product bi-slant submanifolds of Kenmotsu manifold

In this paper, we obtain several fundamental results of bi-slant submanifolds in a Kenmotsu manifold. Next, we give an example of such submanifolds. Later, we obtain some results of proper bi-slant submanifolds of a Kenmotsu manifold. Here, we show every warped product bi-slant submanifold of a Kenmotsu manifold to be a Riemannian product under some certain conditions.