Semi-symmetric Non-metric Connection Research Articles

Constant sectional curvature surfaces with a semi-symmetric non-metric connection

Consider the Euclidean space R3 endowed with a canonical semi-symmetric non-metric connection determined by a vector field C∈X(R3). We study surfaces when the sectional curvature with respect to this connection is constant. In case that the surface is cylindrical, we obtain full classification when the rulings are orthogonal or parallel to C. If the surface is rotational, we prove that the rotation axis is parallel to C and we classify all conical rotational surfaces with constant sectional curvature. Finally, for the particular case 12 of the sectional curvature, the existence of rotational surfaces orthogonally intersecting the rotation axis is also obtained.

A new semi-symmetric non-metric connection on warped products

A new semi-symmetric non-metric connection on warped products

Riemannian manifold admitting a new type of semi-symmetric non-metric connection

We define a new type of semi-symmetric non-metric connection on a Riemannian manifold and established its existence. Further, we find some basic results of curvature tensor and Ricci tensor. It is proved that such connection on a Riemannian manifold is projectively invariant under certain conditions. We also studied some properties of submanifolds of the Riemannian manifolds with respect to the semi-symmetric non-metric connection. To validate our findings, we construct two non-trivial examples of 3-dimensional and 5-dimensional Riemannian manifold equipped with a semi-symmetric non-metric connection.

A Note on a Well-Defined Sectional Curvature of a Semi-Symmetric Non-Metric Connection

In this note we propose a new sectional curvature on a Riemannian manifold endowed with a semi-symmetric non-metric connection. A Chen-Ricci inequality is proven. Some possible applications in other fields are mentioned.

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.

Lorentzian manifolds: A characterization with a type of semi-symmetric non-metric connection

This paper characterizes the Lorentzian manifolds endowed with a semi-symmetric non-metric [Formula: see text]-connection (briefly, ssnmρc). First, the existence of semi-symmetric non-metric connection (ssnmc) on Lorentzian manifold is established, and it is shown that an [Formula: see text]-dimensional Lorentzian manifold equipped with an ssnmρc is a generalized Robertson–Walker spacetime. We also establish the condition for a Lorentzian manifold together with an ssnmρc to be a Robertson–Walker spacetime. In this series, the properties of Ricci semi-symmetric Lorentzian manifold endowed with an ssnmρc, almost Ricci solitons and gradient Ricci solitons are explored. Finally, a non-trivial example of Lorentzian manifold admits an ssnmρc, which is constructed to verify some of our results.

$ \eta $-Ricci-Bourguignon solitons with a semi-symmetric metric and semi-symmetric non-metric connection

<abstract><p>We consider a generalization of a Ricci soliton as $ \eta $-Ricci-Bourguignon solitons on a Riemannian manifold endowed with a semi-symmetric metric and semi-symmetric non-metric connection. We find some properties of $ \eta $-Ricci-Bourguignon soliton on Riemannian manifolds equipped with a semi-symmetric metric and semi-symmetric non-metric connection when the potential vector field is torse-forming with respect to a semi-symmetric metric and semi-symmetric non-metric connection.</p></abstract>

Certain lie algebraic structures on Riemannian manifolds with semi-symmetric non-metric connection

As a natural consequence of the Levi-Civita connection on a Riemannian manifold, there is a Lie algebra structure on a Riemannian manifold. Lie Algebras and Lie Groups are the mathematical structure of continuous symmetries in physics. In this paper, semi-symmetric non-metric connection is considered instead of Levi-Civita connection of Riemann manifold, and accordingly the existence of algebraic structures is investigated. First, it is shown that there is not always a Lie algebra structure on a Riemannian manifold with a semi-symmetric non-metric connection. Then, necessary and sufficient conditions for Lie admissible algebra, pre-Lie algebra and post Lie algebra on a Riemann manifold with semi-symmetric non-metric connection are obtained depending on geometric terms. In addition, the cases of the Riemannian manifold with such algebraic structures according to the semi-symmetric non-metric connection being Einstein manifold and being flat manifold have been also investigated.

Riemannian submersions endowed with a new type of semi-symmetric non-metric connection

In this paper we study relations for the covariant derivative of O?Neill?s tensor fields, Riemannian curvature, Ricci curvature and scalar curvature of the Riemannian submersion from a Riemannian manifold with respect to a new type of semi-symmetric non-metric connection to a Riemannian manifold, respectively, and demonstrate the relationship between them.

Semi-symmetric non-metric connections on statistical manifolds

This study presents a semi-symmetric non-metric connection on statistical manifolds and their submanifolds. The study determines some fundamental properties for the curvature tensor and proves the induced connection on the submanifold with the semi-symmetric non-metric connection. Also, the Gauss, Codazzi, and Ricci equations admitting semi-symmetric non-metric connection have been examined. Finally, a constructive example of such type manifolds is presented.

Super warped products with a semi-symmetric non-metric connection

<abstract><p>In this paper, we define a semi-symmetric non-metric connection on super Riemannian manifolds. And we compute the curvature tensor and the Ricci tensor of a semi-symmetric non-metric connection on super warped product spaces. Next, we introduce two kinds of super warped product spaces with a semi-symmetric non-metric connection and give the conditions that two super warped product spaces with a semi-symmetric non-metric connection are the Einstein super spaces with a semi-symmetric non-metric connection.</p></abstract>

Singular Minimal Surfaces which are Minimal

In the present paper, we discuss the singular minimal surfaces in Euclidean $3-$space $\mathbb{R}^{3}$ which are minimal. Such a surface is nothing but a plane, a trivial outcome. However, a non-trivial outcome is obtained when we modify the usual condition of singular minimality by using a special semi-symmetric metric connection instead of the Levi-Civita connection on $\mathbb{R}^{3}$. With this new connection, we prove that, besides planes, the singular minimal surfaces which are minimal are the generalized cylinders, providing their explicit equations. A trivial outcome is observed when we use a special semi-symmetric non-metric connection. Furthermore, our discussion is adapted to the Lorentz-Minkowski 3-space.

TANGENT BUNDLES ENDOWED WITH SEMI-SYMMETRIC NON-METRIC CONNECTION ON A RIEMANNIAN MANIFOLD

The differential geometry of the tangent bundle is an effective domain of differential geometry which reveals many new problems in the study of modern differential geometry. The generalization of connection on any manifold to its tangent bundle is an application of differential geometry. Recently a new type of semi-symmetric non-metric connection on a Riemannian manifold is studied and established a relationship between Levi-Civita connection and semi-symmetric non-metric connection. The various properties of a Riemannian manifold with relation to such connection are also discussed. The present paper aims to study the tangent bundle of a new type of semi-symmetric non-metric connection on a Riemannian manifold. The necessary and sufficient conditions for projectively invariant curvature tensors corresponding to such connection are proved and show many basic results on the Riemannian manifold in the tangent bundle. Furthermore, the properties of group manifolds of the Riemannian manifolds with respect to the semi-symmetric non-metric connection in the tangent bundle are studied. Moreover, theorems on the symmetry property of Ricci tensor and Ricci soliton in the tangent bundle are established.

Geometry of semi-Riemannian group manifold and its applications in spacetime admitting Ricci solitons

In this work, we show that semi-Riemannian group manifold admits Ricci solitons and satisfies the dynamical cosmology equation of spacetime. In Sec. 2, we introduce and provide some geometric properties of semisymmetric nonmetric connection in semi-Riemannian space. In Sec. 3, we define and show some geometric properties of group manifold endowed with semisymmetric nonmetric connection in semi-Riemannian space. In the section that follows, we give a condition of a group manifold to be Ricci solitons and gradient Ricci soliton. In Sec. 5, we provide the applications of group manifold admitting Ricci solitons in the theory of general relativity.

On a Type of Semi-Symmetric Non-Metric Connection in HSU-Unified Structure Manifold

In the present paper, we have studied some properties of a semi-symmetric non-metric connection in HSU-unified structure manifold and HSU-Kahler manifold. Some new results on such manifolds have been obtained.

Study of Some Properties on Almost Para Contact Metric Manifolds with Certain Connection

Many differential geometers studied different types of manifolds with a semi-symmetric metric connection. In the present paper, we study semi-symmetric nonmetric connections on an almost para-contact manifold in relation to semi-symmetric nonmetric connections. In another section of the work, we have studied the curvature tensor and Nijenhuis tensor.

Semi-Riemannian manifold with semi-symmetric connections

In this paper, we first introduce semi-symmetric metric and semi-symmetric non-metric connections on a n-distribution D of a (n+p)-dimensional semi-Riemannian manifold (M,g). Then we obtain the Gauss equations and the sectional curvature with respect to these connections. Finally, we give an example of a semi-Riemannian manifold with semi-symmetric metric and non-metric connections.

Semi-Invariant Riemannian Submersions with Semi-Symmetric Non-Metric Connection

In this paper, we investigate semi-invariant Riemannian submersion from a Kaehler manifold with semi-symmetric non-metric connection to a Riemannian manifold. We study the geometry of foliations with semi-symmetric non-metric connection. Later, we introduce base manifold to be a local product manifold with semi-symmetric non-metric connection.

Characterization of Lorentzian manifolds with a semi-symmetric linear connection

Our aim is to characterize the Lorentzian manifolds endowed with a type of semi-symmetric non-metric connection. It is proven that a Lorentzian manifold with a type of semi-symmetric non-metric connection is a GRW space-time. To minimize the gap between the RW space-time and the GRW space-time, we establish a bridge between them. It is shown that a weakly Ricci symmetric GRW space-time is a stiff matter fluid. We also classify the space-times by using the Petrov's classification. Finally, we construct an example of a 4-dimensional Lorentzian manifold admitting a semi-symmetric non-metric connection whose associated vector field is a unit timelike concircular vector field.

Super quasi-Einstein warped products with affine connections

In this paper, we study super quasi-Einstein warped product spaces with semi-symmetric non-metric connection and quarter symmetric connection. Then we give the expressions of the Ricci tensors and scalar curvatures for the bases and fibers with these affine connections. Next we find the obstructions to the existence of super quasi-Einstein warped products with respect to affine connections. In the last section, we obtain an example of super quasi-Einstein space time.