Tangent Bundles Endowed with Quarter-Symmetric Non-Metric Connection (QSNMC) in a Lorentzian Para-Sasakian Manifold

Abstract

The purpose of the present paper is to study the complete lifts of a QSNMC from an LP-Sasakian manifold to its tangent bundle. The lifts of the curvature tensor, Ricci tensor, projective Ricci tensor, and lifts of Einstein manifold endowed with QSNMC in an LP-Sasakian manifold to its tangent bundle are investigated. Necessary and sufficient conditions for the lifts of the Ricci tensor to be symmetric and skew-symmetric and the lifts of the projective Ricci tensor to be skew-symmetric in the tangent bundle are given. An example of complete lifts of four-dimensional LP-Sasakian manifolds in the tangent bundle is shown.

Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold

“…The studies on gradient estimates and differential Harnack inequalities were presented in [6][7][8][9][10][11]. We can find some papers regarding different manifolds of different connections in a tangent bundle [12][13][14][15][16][17][18]. All of these papers provide powerful mathematical tools for comprehending manifold evolution and changes, contributing to the derivation of numerous mathematical theorems and results.…”

Lifts of a Semi-Symmetric Metric Connection from Sasakian Statistical Manifolds to Tangent Bundle

“…Yano and Ishihara [13] established the lifts of the manifold, as well as the connection in the tangent bundle. Different manifolds associated with different connections in the tangent bundle were studied in [16][17][18][19][20][21][22][23][24]. Kumar et al [25] recently studied the lifts of the semi-symmetric non-metric connection (SSNMC) from statistical manifolds to the tangent bundle.…”

Proposed Theorems on the Lifts of Kenmotsu Manifolds Admitting a Non-Symmetric Non-Metric Connection (NSNMC) in the Tangent Bundle

“…In an n-dimensional manifold M n , if the torsion tensor T of the linear connection ∇ satisfies T(X 0 , Y 0 ) = 2g(ΦX 0 , Y 0 ), it is called a non-symmetric connection for all vector fields X 0 , Y 0 on M n and, additionally, if the Riemannian metric g is such that ∇g = 0, then it is called a metric connection, and it is called non-metric if ∇g = 0. Different geometers have studied and defined different types of connections, which can be seen in [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”