Tangent Bundles Endowed with Quarter-Symmetric Non-Metric Connection (QSNMC) in a Lorentzian Para-Sasakian Manifold
Rajesh Kumar, Lalnunenga Colney, Sameh Shenawy, Nasser Bin Turki
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.
Topics & Concepts
Tangent bundleRicci curvatureMathematicsRicci decompositionMetric connectionPure mathematicsRiemann curvature tensorMathematical analysisManifold (fluid mechanics)Normal bundleConnection (principal bundle)CurvatureVector bundleTangent spaceGeometryFundamental theorem of Riemannian geometryEngineeringMechanical engineeringGeometric Analysis and Curvature FlowsAdvanced Differential Geometry ResearchGeometry and complex manifolds