Certain results on Lorentzian para-Kenmotsu manifolds
Abdul Haseeb, Rajendra Prasad
Abstract
The object of the present paper is to study Lorentzian para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection. First we study Lorentzian para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection satisfying the conditions $\bar R\cdot \bar S=0$ and $\bar S\cdot \bar R=0$. After that we study $\phi$-conformally flat, $\phi$-conharmonically flat, $\phi$-concircularly flat, $\phi$-projectively flat and conformally flat Lorentzian para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection and it is shown that in each of these case the manifold is generalized $\eta$-Einstein manifold.
Topics & Concepts
Connection (principal bundle)Manifold (fluid mechanics)Bar (unit)Metric (unit)Metric connectionQuarter (Canadian coin)Pure mathematicsEinsteinMathematicsMathematical analysisPhysicsGeometryMathematical physicsCurvatureScalar curvatureFundamental theorem of Riemannian geometryEngineeringOperations managementMechanical engineeringMeteorologyArchaeologyHistoryGeometric Analysis and Curvature FlowsAdvanced Differential Geometry ResearchGeometry and complex manifolds