希尔伯特第四问题的周期解

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2021-10-22 DOI:10.1142/s1793525321500552

J. C. Álvarez Paiva, J. Barbosa Gomes

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引用次数: 0

摘要

证明了一个可能不可逆的[公式:见文]在环面或任何其他紧致欧几里得空间形式上，其测地线为直线的芬斯勒度规是一个平面度规和一个封闭的[公式:见文]-形式的和。这被用来证明如果[公式:见文]是秩大于1的紧黎曼对称空间，且[公式:见文]是可逆的[公式:见文]上的[公式:见文]的非参测大地线与[公式:见文]的非参测大地线一致的[公式:见文]的芬斯勒度量，则[公式:见文]是一个芬斯勒对称空间。

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Periodic solutions of Hilbert’s fourth problem

It is shown that a possibly irreversible [Formula: see text] Finsler metric on the torus, or on any other compact Euclidean space form, whose geodesics are straight lines is the sum of a flat metric and a closed [Formula: see text]-form. This is used to prove that if [Formula: see text] is a compact Riemannian symmetric space of rank greater than one and [Formula: see text] is a reversible [Formula: see text] Finsler metric on [Formula: see text] whose unparametrized geodesics coincide with those of [Formula: see text], then [Formula: see text] is a Finsler symmetric space.

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来源期刊

Journal of Topology and Analysis MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.