Sectional curvatures on Weyl manifolds with a special metric connection

Abstract

In this paper, Weyl manifolds, denoted by WS(g, w, π, µ) , having a special a semisymmetric recurrent- metric connection are introduced and the uniqueness of this connection is proved. We give an example of WS(g, w, π, µ) with a constant scalar curvature. Furthermore, we define sectional curvatures of WS(g, w, π, µ) and prove that any isotropic Weyl manifold WS(g, w, π, µ) is locally conformal to an Einstein manifold with a semisymmetric recurrent- metric connection, EWS(g, w, π, µ) .