On Generalized Douglas - Kropina Spaces
S. Ceyhan *
Department of Computer Engineering, Bilecik Seyh Edebali University 11210, Bilecik, Turkey.
G. Çivi
Department of Mathematics, Istanbul Technical University 34469, Istanbul, Turkey.
*Author to whom correspondence should be addressed.
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.
Keywords: Douglas-Weyl metric, kropina metric, scalar flag curvature, Weyl metric.