On Matsumoto metrics of special Ricci tensor

Document Type : Regular Paper


1 Faculty of Science, Department of Mathematics, Urmia University, Urmia, Iran

2 Faculty of science, Department of Mathematics Mazandaran University, P.O. Box 47416-1467, Babolsar, Iran


In this paper, the Matsumoto metric with special Ricci tensor has been investigated. It is proved that, if  is of
positive (negative) sectional curvature and F is of  -parallel Ricci curvature with constant killing 1-form ,
then (M,F) is a Riemannian Einstein space. In fact, we generalize the Riemannian result established by Akbar-