Quarter-symmetric Non-metric Connection Research Articles

Quarter-Symmetric Non-Metric Connection of Non-Integrable Distributions

In this paper, we focus on non-integrable distributions with a quarter-symmetric non-metric connection (QSNMC) in generalized Riemannian manifold. First, by studying a quarter-symmetric connection on the generalized Riemannian manifold, we obtain the condition that the connection is non-metric. Then, the Gauss, Codazzi and Ricci equations are proved for non-integrable distributions with respect to a quarter-symmetric non-metric connection in generalized Riemannian manifold. Furthermore, we deduce Chen’s inequalities for non-integrable distributions of real space forms with a quarter-symmetric non-metric connection in generalized Riemannian manifold as applications. After that, we give some examples of non-integrable distributions in Riemannian manifold with quarter-symmetric non-metric connection.

SOME RESULTS ON YAMABE SOLITONS ON NEARLY HYPERBOLIC SASAKIAN MANIFOLDS

We classify almost Yamabe on nearly hyperbolic Sasakian manifolds whose potential vector field is torse-forming admitting semi-symmetric metric connection and quarter symmetric non-metric connection. Certain results of such solitons on CR-submanifolds of nearly hyperbolic Sasakian manifolds with respect to such connection are obtained. Finally, a non-trivial example is given to validate some of our results.

On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed with a Quarter-Symmetric Non-metric Connection

The object of this article is to study a quarter-symmetric non-metric connection in the tangent bundle and induced metric and connection on submanifold of co-dimension 2 and hypersurface concerning the quarter-symmetric non-metric connection in the tangent bundle. The Weingarten equations concerning the quarter-symmetric non-metric connection on a submanifold of co-dimension 2 and the hypersurface in the tangent bundle are obtained. Finally, authors deduce the Riemannian curvature tensor and Gauss and Codazzi equations on a submanifold of co-dimension 2 and hypersurface of the Riemannian manifold concerning the quarter-symmetric non-metric connection in the tangent bundle.

QUARTER SYMMETRIC NON-METRIC CONNECTION ON A (k, μ)−CONTACT METRIC MANIFOLD

The object of the present paper is to introduce a new type of quartersymmetric non-metric connection on a (k, μ)−contact metric manifold and studysome properties of quarter symmetric non-metric connection on a (k, μ)−contactmetric manifold. Further, we obtain some properties of nearly Ricci recurrent ona (k, μ)−contact metric manifold with respect to quarter symmetric non-metricconnection. Finally, we present an example to verify our result.

Geometries and topologies of a manifold with π-quarter-symmetric projective conformal and mutual connections

We propose a new ?-quarter-symmetric projective conformal connection family and its mutual connection family and study its geometrical properties. We also arrive at the Schur?s theorem based on a symmetric-type ?-quarter-symmetric non-metric connection and investigate its geometrical property. This paper will pose a new grid computing method on manifolds, which will be done in our next topic.

Liftings from a para-Sasakian manifold to its tangent bundles

The purpose of the present paper is to study the liftings of a quarter symmetric non-metric connection from a para-Sasakian manifold to its tangent bundles. By liftings, some results of the curvature tensor, projective curvature tensor, concircular curvature tensor and conformal curvature tensor wrt a quarter symmetric non-metric connection in a P-Sasakian manifold to its tangent bundles are obtained.

STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold with a Quarter Symmetric Non-Metric Connection

The present work aims to introduce a novel class of submanifolds, namely STCR-lightlike submanifolds, for an indefinite Kaehler statistical manifold with a quarter symmetric non-metric connection. The characterization theorems on totally umbilical and totally geodesic STCR-lightlike submanifolds with respect to the integrability of distributions have been established. Some conditions for a STCR-lightlike submanifold to be a STCR-lightlike product manifold have been derived.

Contact CR-submanifolds of trans-Sasakian manifolds with respect to quarter symmetric non-metric connection

The present paper deals with the study of contact CR-submanifolds of trans-Sasakian manifolds with respect to quarter symmetric non-metric connection. We investigate totally geodesic leaves and integrability of the distributions and also study the totally umbilical contact CR-submanifolds of trans-Sasakian manifolds. At last we give an example to verify a relation.

On GCR-Lightlike Submanifolds of Indefinite Kaehler Manifolds

We study generalized Cauchy-Riemann (GCR)-lightlike submanifolds of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection. We derive a condition for a totally umbilical GCR-lightlike submanifold of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection to be a totally geodesic submanifold. We study minimal GCR-lightlike submanifolds and obtain characterization theorem for a GCR-lightlike submanifold to be a GCR-lightlike product manifold.

Different Types of Curvature and Their Vanishing Conditions

In the present paper, I studied different types of Curvature like Riemannian Curvature, Concircular Curvature, Weyl Curvature, and Projective Curvature in Quarter Symmetric non-Metric Connection in P-Sasakian manifold. A comparative study of a manifold with a Riemannian connection is done with a P-Sasakian Manifold. Conditions for vanishing for different types of curvature are also a part of the study. Some necessary properties of the Hessian operator are discussed with respect to all curvatures as well.

Riemannian Submersions with Quarter- Symmetric Non-Metric Connection

In this paper, we study Riemannian submersions from a Riemannian manifold endowed with a quarter-symmetric non-metric connection onto a Riemannian manifold. We investigate O’Neill’s tensor fields for quarter-symmetric non-metric connection and derive the covariant derivative of O’Neill’s tensor fields. We obtain derivatives of those tensor fields and compare curvatures of the total manifold, the base manifold, and the fibers by computing curvatures.

ON φˇ-SEMISYMMETRIC LP-KENMOTSU MANIFOLDS WITH A QSNM-CONNECTION ADMITTING RICCI SOLITONS

Abstract. In the present work, we characterize Lorentzian para-Kenmotsu (briefly, LP-Kenmotsu) manifolds with a quarter-symmetric non-metric connection (briefly, QSNM-connection) ∇b satisfying certain φ¨-semisymmetric conditions admitting Ricci solitions. At the end of the paper, a 3-dimensional example of LP-Kenmotsu manifolds with a connection ∇b is given to verify some results of the present paper.

$\eta$-Ricci solitons on trans-Sasakian manifolds with quarter-symmetric non-metric connection

$\eta$-Ricci solitons on trans-Sasakian manifolds with quarter-symmetric non-metric connection

Study of Hypersurface of semi-almost Hermitian manifold equipped with quarter-symmetric non-metric connection

In this paper, an induced connection on a Hyper surface ofa semi-almost Hermitian manifold equipped with a quarter-symmetric non-metric connection is studied and proved that induced connection is also a quarter-symmetricnon-metric connection.Further, we have obtained We ingarten equation, equation of Gauss curvature and the Codazzi Main ardiequation of hyper surface of a semi-almost Hermitian manifold equipped with a quarter-symmetric non-metric connection. AMS Mathematics Subject Classification (2010): 53C07,53C26,53C42,53C55

TANGENT BUNDLE ENDOWED WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION ON AN ALMOST HERMITIAN MANIFOLD

In this paper, we have studied the tangent bundle endowed with quarter-symmetric non-metric connection obtained by vertical and complete lifts of a quarter-symmetric non-metric connection on the base manifold and, also, proposed the study of the tangent bundle of an almost Hermitian manifold and an almost Kaehler manifold. Finally, we obtained some theorems for Nijenhuis tensor on the tangent bundle of an almost Hermitian manifold and an almost Kaehler manifold.\\

Some properties of trans Sasakian manifolds admitting a quarter-symmetric non-metric connection

Some properties of trans Sasakian manifolds admitting a quarter-symmetric non-metric connection

Characterization of the Lorentzian para-Sasakian manifolds admitting a quarter-symmetric non-metric connection

We set the goal to study the properties of LP-Sasakian manifolds equipped with a quarter-symmetric non-metric connection. It is proved that the LP-Sasakian manifold endowed with a quarter-symmetric non-metric connection is partially Ricci semisymmetric with respect to the quarter-symmetric non-metric connection if and only if it is an η-Einstein manifold. We also study the properties of semisymmetric, Ricci recurrent LP-Sasakian manifolds and η-parallel Ricci tensor with respect to the quarter-symmetric non-metric connection. In the end, the non-trivial example of a 4-dimensional LP-Sasakian manifold with a quarter-symmetric non-metric connection is given.

On concircular curvature tensor in a Lorentzian α-Sasakian manifold with respect to the quarter-symmetric non-metric connection

In the present paper, some properties of concircular curvature tensor in a Lorentzian α-Sasakian manifold with respect to the quarter-symmetric non-metric connection have been studied.

On submanifolds of an almost contact metric manifold admitting a quarter-symmetric non-metric connection

We study submanifolds of an almost contact metric manifold admitting a quarter-symmetric non-metric connection. We prove the induced connection on a submanifold is also quarter-symmetric non-metric connection. We consider the total geodesicness and minimality of a submanifold with respect to the quarter-symmetric non-metric connection. We obtain the Gauss, Cadazzi and Ricci equations for submanifolds with respect to the quarter-symmetric non-metric connection and show some applications of these equations. Finally, we give two examples verifying the results

CR-submanifolds of (LCS)n-manifolds with respect to quarter symmetric non-metric connection

The present paper deals with the study of CR-submanifolds of (LCS)n-manifolds with respect to quarter symmetric non-metric connection. We investigate integrability of the distributions and the geometry of foliations. The totally umbilical CR-submanifolds of said ambient manifolds are also studied. An example is presented to illustrate the results.