Symmetric Non-metric Connection Research Articles

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.

Investigations on a Riemannian Manifold with a Semi- Symmetric Non-Metric Connection and Gradient Solitons

This article carries out the investigation of a three-dimensional Riemannian manifold N3 endowed with a semi-symmetric type non-metric connection. Firstly, we construct a non-trivial example to prove the existence of a semi-symmetric type non-metric connection on N3. It is established that a N3 with the semi-symmetric type non-metric connection, whose metric is a gradient Ricci soliton, is a manifold of constant sectional curvature with respect to the semi-symmetric type non-metric connection. Moreover, we prove that if the Riemannian metric of N3 with the semi-symmetric type non-metric connection is a gradient Yamabe soliton, then either N3 is a manifold of constant scalar curvature or the gradient Yamabe soliton is trivial with respect to the semi-symmetric type non-metric connection. We also characterize the manifold N3 with a semi-symmetric type non-metric connection whose metrics are Einstein solitons and m-quasi Einstein solitons of gradient type, respectively.

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.

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.

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.

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.

P-Sasakian Manifold with Quarter-Symmetric Non-Metric Connection

The object of the present paper is to study on a P-Sasakian manifold with quarter symmetric non-metric connection. In this paper, we consider some properties of the curvature tensor, projective curvature tensor, concircular curvature tensor, conformal curvature tensor with respect to quarter symmetric non-metric connection in a P-Sasakian manifolds. Finally, we give an example.

On φ-pseudo symmetric LP-Sasakian manifolds with respect to quarter-symmetric non-metric connections

The object of the present paper is to study φ-pseudo symmetric and φ-pseudo Ricci symmetric LP-Sasakian manifolds with respect to Levi–Civita connections and quarter-symmetric non-metric connections. We obtain a necessary and sufficient condition for a φ-pseudo symmetric LP-Sasakian manifold with respect to a quarter symmetric non-metric connection to be φ-pseudo symmetric LP-Sasakian manifold with respect to a Levi–Civita connection.

Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection

We study lightlike submanifolds of a semi-Riemannian product manifold. We introduce a class of lightlike submanifolds called screen semi-invariant lightlike submanifold. We consider lightlike submanifolds with respect to a quarter symmetric non-metric connection which is determined by the product structure. We give some equivalent conditions for integrability of distributions with respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric nonmetric connection, and we obtain some results.

Lorentzian para-Sasakian manifold with quarter-symmetric non-metric connection

The object of the present paper is to study quarter symmetric nonmetric connection on a LP-Sasakian manifold. In this paper, we consider some properties of the curvature tensor, projective curvature tensor, concircular curvature tensor, conformai curvature tensor with respect to quarter symmetric non-metric connection in a LP-Sasakian manifolds. Finally we consider submanifolds with respect to quarter symmetric non-metric connection.

CR-submanifolds of a nearly trans-hyperbolic Sasakian manifold with a quarter symmetric non-metric connection

This paper deals with the study of CR-submanifolds of a nearly trans-hyperbolic Sasakian manifold with a quarter symmetric non-metric connection. We study parallel distribution relating to

On semi-invariant submanifolds of a nearly Sasakian manifold with a quarter symmetric non-metric connection

On semi-invariant submanifolds of a nearly Sasakian manifold with a quarter symmetric non-metric connection

Some Properties of <i>CR</i>-Submanifolds of a Nearly Trans-Sasakian Manifold with a Semi Symmetric Non-Metric Connection

This paper deals with the study of CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non-metric connection. Nijenhuis tensor, integrability conditions for some distributions on CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non- metric connection are discussed.

ON SEMI-INVARIANT SUBMANIFOLDS OF A NEARLY KENMOTSU MANIFOLD WITH A QUARTER SYMMETRIC NON-METRIC CONNECTION

We define a quarter symmetric non-metric connection in a nearly Kenmotsu manifold and we study semi-invariant submanifolds of a nearly Kenmotsu manifold endowed with a quarter symmetric non-metric connection. Moreover, we discuss the integrability of the distributions on semi-invariant submanifolds of a nearly Kenmotsu manifold with a quarter symmetric non-metric connection.

Hypersurfaces of an almost r-paracontact Riemannian Manifold Endowed with a Quarter Symmetric Non-metric Connection

We define a quarter symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric non-metric connection.

Generlized Quasi-Sasakian Manifold admitting Semi-Symmetric Non Metric Connection

Agashe and Chafle [4] defined a semi – symmetric non-etric connection in a Riemannian manifold. Further, the properties of semi- symmetric non-metric connection in almost contact metric manifold has been studied by Ojha and Prasad [5]. The purpose of this paper is to introduce a semi-symmetric non-metric connection in generalized quasi-sasakian manifold.

Characterization of Quarter Symmetric Non-Metric Connection on Transversal Hypersurfaces of Lorentzian para-Sasakian Manifolds

In the present paper, quarter symmetric non metric connection on transversal hypersurfaces of Lorentzian para-Sasakian manifold is defined. It is studied the characterization of connections for product structure and it is shown that each transversal hypersurfaces of Lorentzian para-Sasakian manifold admits an almost product Lorentzian structure on a quarter symmetric non metric connection. Some characterization of transversal hypersurfaces of Lorentzian paraSasakian manifold with a quarter symmetric non metric connection are studied which are closed.