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

2013/10/13 by Guojun Yang, Yang, Guojun · 1 citation
Physics and Astronomy · #53B40 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1310.3463

openalex publication_date 2013/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An (α,β)-metric is defined by a Riemannian metric and 1-form. In this paper, we investigate the known characterization for (α,β)-metrics of isotropic S-curvature. We show that such a characterization should hold in dimension n≥ 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 β with respect to α is not a constant.

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

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