A Note on a Class of Finsler Metrics of Isotropic S-Curvature

Abstract

An $(\alpha ,\beta )$-metric is defined by a Riemannian metric and $1$-form. In this paper, we investigate the known characterization for $(\alpha ,\beta )$-metrics of isotropic S-curvature. We show that such a characterization should hold in dimension $n\ge 3$, and for the 2-dimensional case, there is one more class of isotropic S-curvature than the higher dimensional ones. Further, we construct corresponding examples for every two-dimensional class, especially for the class that the norm of $\beta$ with respect to $\alpha$ is not a constant.

arXiv comment14 pages

References in corpus (1)

• On A Class of Finsler Metrics of Einstein-Reversibility

Cited by in corpus (1)

• On a Class of Two-Dimensional Einstein Finsler Metrics of Vanishing S-Curvature