Periodic solutions of Hilbert’s fourth problem
| Autor: | J. C. Álvarez Paiva, J. Barbosa Gomes |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Geodesic Euclidean space Computer Science::Information Retrieval Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Torus Hilbert's fourth problem Metric (mathematics) Computer Science::General Literature Mathematics::Differential Geometry Geometry and Topology Analysis Mathematics |
| Zdroj: | Journal of Topology and Analysis. :1-20 |
| ISSN: | 1793-7167 1793-5253 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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