2022/05/24 by Guojun Yang, Yang, Guojun
Physics and Astronomy · #53B40 #53C60 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2205.11892
openalex publication_date 2022/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Every Finsler metric naturally induces a spray but not so for the converse. The notion for sprays of scalar (resp. isotropic) curvature has been known as a generalization for Finsler metrics of scalar (resp. isotropic) flag curvature. In this paper, a new notion, sprays of constant curvature, is introduced and especially it shows that a spray of isotropic curvature is not necessarily of constant curvature even in dimension n≥3. Further, complete conditions are given for sprays of isotropic (resp. constant) curvature to be Finsler-metrizabile. As applications of such a result, the local structure is determined for locally projectively flat Berwald sprays of isotropic (resp. constant) curvature which are Finsler-metrizable, and some more sprays of isotropic curvature are discussed for their metrizability. Besides, the metrizability problem is also investigated for sprays of scalar curvature under certain curvature conditions.