Chapter2 2 2. Perspective Chapter: Quasi Conformally Flat Quasi Einstein-Weyl Manifolds

Abstract The aim of this work is to study on quasi conformally flat quasi Einstein-Weyl manifolds. In this book chapter, firstly, an interesting relationship between complementary vector field and generator of the quasi Einstein-Weyl manifold is obtained and supported by an example. Then, it is investigated that quasi conformally flat quasi Einstein-Weyl manifolds are of quasi constant curvature, recurrent and semi-symmetric under which conditions after obtaining the expression of the curvature tensor of the quasi conformally flat quasi Einstein-Weyl manifold. Furthermore, some equivalences are obtained between to be of quasi constant curvature and to be semi-symmetric in quasi conformally flat quasi Einstein-Weyl manifolds.