Study of W6-Curvature Tensor on Lorentzian Para-Sasakian Manifolds and Other Related Manifolds

Abstract

In this research we study W6 curvature tensor on Lorentzian para Sasakian Manifold and other related Manifold where curvature tensor have been defined on the lines of Weyls projective curvature tensor.It has been shown that distri- bution (order in which the vectors in question are arranged before being acted upon by the tensor in question) of vector field over the metric potential and matter tensor plays an important role in shaping various physical and geometri- cal properties of a tensor and the formulation of gravitational waves,reduction of electromagnetic field to a purely electric field,vanishing of the contracted tensor in an Einstein space and cyclic property. The study deals with curva- ture tensor of Semi-Riemannian and generalized Sasakian space forms admitting Semi-symmetric metric connection. More specifically, we study the geometry of Semi-Rienmannian and generalized Sasakian space forms when they are W6- flat,W6-Symmetric,W6-Semi Symmetric and W6-Recurrent and compared to re- sult of projectively Semi-Symmetric, Weyl’s Semi-Symmetric and concircularly Semi-Symmetric on these spaces. Our main methodology will be use of defini- tions,manifold transformation and covariant differentiation. This study will add applicable knowledge in mathematics,physics and chemistry in the analysis of cur- vature tensor to generate equations which describe the nature of forces existing in black holes,spinning planets,Electrons and Protons in atoms.