On a Class of Ricci Quadratic Finsler Metrics

Abstract

In this paper, we study a class of Finsler warped product metrics with quadratic Ricci curvature. This class is characterized by a partial differential equation. In particular, we obtain a special class of Finsler warped product metrics with quadratic Ricci curvature, indeed, the metrics in this class are Einstein but not Ricci flat. We find an equation that characterizes Finsler warped product metrics as a strongly Ricci-quadratic.