Certain Results on the Lifts from an LP-Sasakian Manifold to Its Tangent Bundle Associated with a Quarter-Symmetric Metric Connection (original) (raw)
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Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle
Mathematics
The objective of this paper is to explore the complete lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle. A relationship between the Riemannian connection and the quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle was established. Some theorems on the curvature tensor and the projective curvature tensor of a Sasakian manifold with respect to the quarter-symmetric metric connection to its tangent bundle were proved. Finally, locally ϕ-symmetric Sasakian manifolds with respect to the quarter-symmetric metric connection to its tangent bundle were studied.
2019
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. AMS 2010 Mathematics Subject Classification. 53D10, 53C25, 53D15.
Some notes on LPLPLP-Sasakian Manifolds with Generalized Symmetric Metric Connection
Cornell University - arXiv, 2018
The present study initially identify the generalized symmetric connections of type (α, β), which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when (α, β) = (1, 0) and (α, β) = (0, 1). Taking that into account, a new generalized symmetric metric connection is attained on Lorentzian para-Sasakian manifolds. In compliance with this connection, some results are obtained through calculation of tensors belonging to Lorentzian para-Sasakian manifold involving curvature tensor, Ricci tensor and Ricci semi-symmetric manifolds. Finally, we consider CR-submanifolds admitting a generalized symmetric metric connection and prove many interesting results.
Quarter-symmetric metric connection on a Lorentzian alpha-Sasakian manifold
New Trends in Mathematical Science
In the present paper we study locally φ-symmetric, locally projective φ-symmetric, φ-recurrent and φ-projectively flat Lorentzian α-Sasakian manifold with respect to quarter-symmetric metric connection. Further, the existence of a Lorentzian α-Sasakian manifold admitting quarter-symmetric metric connection is shown by constructing an example.
Some Classes of Lorentzian α-Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection
2017
The object of the present paper is to study a quarter-symmetric metric connection in an Lorentzian α-Sasakian manifold. We study some curvature properties of an Lorentzian α-Sasakian manifold with respect to the quarter-symmetric metric connection. We study locally φ-symmetric, φsymmetric, locally projective φ-symmetric, ξ-projectively flat Lorentzian α-Sasakian manifold with respect to the quarter-symmetric metric connection.
Some classes of Lorentzian α-Sasakian manifolds with respect to quarter-symmetric metric connection
Tbilisi Mathematical Journal, 2017
The object of the present paper is to study a quarter-symmetric metric connection in a Lorentzian α-Sasakian manifold. We study some curvature properties of Lorentzian α-Sasakian manifold with respect to quarter-symmetric metric connection. We investigate quasi-projectively at, ϕ-symmetric, ϕ-projectively at Lorentzian α-Sasakian manifolds with respect to quartersymmetric metric connection. We also discuss Lorentzian α-Sasakian manifold admitting quarter-symmetric metric connection satisfying P̃.S̃ = 0, where P̃ denote the projective curvature tensor with respect to quarter-symmetric metric connection.
On LP-Sasakian manifold admitting a generalized symmetric metric connection
Malaya Journal of Matematik
In this paper we study certain curvature properties of Lorentzian Para-Sasakian manifold (shortly, LPSM) with respect to the generalized symmetric metric connection. Here we discuss ξ-concircularly, ξ-conformally and ξprojectively flat LPSM with respect to the generalized symmetric metric connection and obtain various interesting results. Moreover, we study LPSM withZ(ξ ,V).S = 0, whereZ andS are the concircular curvature tensor and Ricci tensor respectively with respect to the generalized symmetric metric connection.