Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle
Mohammad Nazrul Islam Khan, Uday Chand De, Ljubica S. Velimirović
Abstract
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.
Topics & Concepts
Tangent bundleMetric connectionConnection (principal bundle)MathematicsUnit tangent bundleLevi-Civita connectionNormal bundleMathematical analysisFundamental theorem of Riemannian geometryMetric (unit)Manifold (fluid mechanics)Pure mathematicsCurvatureRiemann curvature tensorRicci curvatureTopology (electrical circuits)GeometryCombinatoricsTangent spaceVector bundleEngineeringMechanical engineeringEconomicsOperations managementGeometric Analysis and Curvature FlowsAdvanced Differential Geometry ResearchGeometry and complex manifolds