Spherically symmetric Finsler metrics with Scalar Flag Curvature

Authors: WEIDONG SONG, FEN ZHOU

Abstract: In this paper, we study spherically symmetric Finsler metrics F=|y|\phi(|x|,\frac{}{|y|}), where x \in B^n(r) \subset R^n, y \in T_xB^n(r)\{0} and \phi:[0,r)\times R \rightarrow R. By investigating a PDE equivalent to these metrics being locally projectively flat, we manufacture projectively flat spherically symmetric Finsler metrics in terms of error functions and, using Shen's result, we give its flag curvature.

Keywords: Spherically symmetric, locally projectively flat, scalar flag curvature, error function

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