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On Sakaguchi-type result in projective spray geometry

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Abstract

We know that there are infinitely many sprays of scalar curvature which cannot be induced by any (not necessary positive definite) Finsler metric. In this paper, we show that every spray of scalar curvature satisfies the following: the rate of change of the Douglas curvature along a geodesic is tangent to the geodesic, generalizing Sakaguchi result previously known only when the spray is induced by a positive definite Finsler metric.

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Authors and Affiliations

  1. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310023, China

    Ying Li

  2. Key Laboratory of Pure and Applied Mathematics School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Xiaohuan Mo

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  1. Ying Li
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  2. Xiaohuan Mo
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Correspondence to Xiaohuan Mo.

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Xiaohuan Mo: Supported by the National Natural Science Foundation of China 11371032.

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Li, Y., Mo, X. On Sakaguchi-type result in projective spray geometry. Annali di Matematica 200, 2181–2189 (2021). https://doi.org/10.1007/s10231-021-01074-w

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  • DOI: https://doi.org/10.1007/s10231-021-01074-w

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