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- W4281569275 abstract "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 $nge3$. 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." @default.
- W4281569275 created "2022-05-27" @default.
- W4281569275 creator A5060811534 @default.
- W4281569275 date "2022-05-24" @default.
- W4281569275 modified "2023-09-24" @default.
- W4281569275 title "On Sprays of Scalar Curvature and Metrizability" @default.
- W4281569275 doi "https://doi.org/10.48550/arxiv.2205.11892" @default.
- W4281569275 hasPublicationYear "2022" @default.
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