On Generalized Douglas - Kropina Spaces

Abstract

Sakaguchi proved that the class of Weyl metrics belong to the class of generalized Douglas–Weyl metric. Then, Matsumoto studied Weyl–Kropina metric. Recently, Yoshikawa and Okubo obtained the conditions for a Kropina space to be of constant curvature by improving the characterization given by M.Matsumoto. In this paper, we obtain the necessary and sufficient conditions for a Kropina metric to be scalar flag curvature or Weyl-Kropina metric. After that, we prove a necessary and sufficient condition that characterizes generalized Douglas-Kropina metrics of scalar flag curvature.