Some classes of 3-dimensional Trans-Sasakian manifolds with respect to semi-symmetric metric connection

The object of the present paper is to study semi-symmetric metric connection on a 3-dimensional trans-Sasakian manifold. We found the necessary condition under which a vector field on a 3-dimensional trans-Sasakian manifold will be a strict contact vector field. Then, we obtained extended generalized phi-recurrent 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection. Next, a 3-dimensional trans-Sasakian manifold satises the condition ~L.~ S = 0 with respect to semi-symmetric metric connection is studied.

A Note on LP -Sasakian Manifolds with Almost Quasi-Yamabe Solitons

We categorize almost quasi-Yamabe solitons on LP -Sasakian manifolds and their CR -submanifolds whose potential vector field is torse-forming, admitting a generalized symmetric metric connection of type α , β . Finally, a nontrivial example is provided to confirm some of our results.

Geometry of α-Cosymplectic Metric as ∗-Conformal η-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection

The outline of this research article is to initiate the development of a ∗-conformal η-Ricci–Yamabe soliton in α-Cosymplectic manifolds according to the quarter-symmetric metric connection. Here, we have established some curvature properties of α-Cosymplectic manifolds in regard to the quarter-symmetric metric connection. Further, the attributes of the soliton when the manifold gratifies a quarter-symmetric metric connection have been displayed in this article. Later, we picked up the Laplace equation from ∗-conformal η-Ricci–Yamabe soliton equation when the potential vector field ξ of the soliton is of gradient type, admitting quarter-symmetric metric connection. Next, we evolved the nature of the soliton when the vector field’s conformal killing reveals a quarter-symmetric metric connection. We show an example of a 5-dimensional α-cosymplectic metric as a ∗-conformal η-Ricci–Yamabe soliton acknowledges quarter-symmetric metric connection to prove our results.

On W0 and W2 ø-Symmetric Contact Manifold Admitting Quarter-Symmetric Metric Connection

The paper deals locally W0 and W2 curvature tensor of ø-symmetric K-contact manifolds with quarter-symmetric metric connection and some results are obtained.

Chen-Ricci Inequalities with a Quarter Symmetric Connection in Generalized Space Forms

In this article, we obtain improved Chen-Ricci inequalities for submanifolds of generalized space forms with quarter-symmetric metric connection, with the help of which we completely characterized the Lagrangian submanifold in generalized complex space form and a Legendrian submanifold in a generalized Sasakian space form. We also discuss some geometric applications of the obtained results.

SOME VECTORS FIELDS ON THE TANGENT BUNDLE WITH A SEMI-SYMMETRIC METRIC CONNECTION

Let $M$ is a (pseudo-)Riemannian manifold and $TM$ be its tangent bundlewith the semi-symmetric metric connection $\overline{\nabla }$. In thispaper, we examine some special vector fields, such as incompressible vectorfields, harmonic vector fields, concurrent vector fields, conformal vectorfields and projective vector fields on $TM$ with respect to thesemi-symmetric metric connection $\overline{\nabla }$ and obtain someproperties related to them.

On Golden Lorentzian Manifolds Equipped with Generalized Symmetric Metric Connection

This research deals with the generalized symmetric metric U-connection defined on golden Lorentzian manifolds. We also derive sharp geometric inequalities that involve generalized normalized δ-Casorati curvatures for submanifolds of golden Lorentzian manifolds equipped with generalized symmetric metric U-connection.

Inequalities on Generalized Sasakian Space Forms

In this paper, we find the second variational formula for a generalized Sasakian space form admitting a semisymmetric metric connection. Inequalities regarding the stability criteria of a compact generalized Sasakian space form admitting a semisymmetric metric connection are established.