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pro vyhledávání: '"Hilbert's Fourth Problem"'
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It is shown that a possibly irreversible $C^2$ 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 $1$-form. This is used to prove that if $(M,g)$ is a
Externí odkaz:
http://arxiv.org/abs/1809.02783
Autor:
Bucataru, Ioan, Muzsnay, Zoltán
Publikováno v:
Journal of the Australian Mathematical Society, vol. 97, 01 (2014), pp. 27-47
It is well known that a system of homogeneous second-order ordinary differential equations (spray) is necessarily isotropic in order to be metrizable by a Finsler function of scalar flag curvature. In Theorem 3.1 we show that the isotropy condition,
Externí odkaz:
http://arxiv.org/abs/1303.5832
Autor:
Papadopoulos, Athanase
Hilbert's fourth problem asks for the construction and the study of metrics on subsets of projective space for which the projective line segments are geodesics. Several solutions of the problem were given so far, depending on more precise interpretat
Externí odkaz:
http://arxiv.org/abs/1312.3172
Autor:
Paiva, Juan-Carlos Alvarez
In the asymmetric setting, Hilbert's fourth problem asks to construct and study all (non-reversible) projective Finsler metrics: Finsler metrics defined on open, convex subsets of real projective $n$-space for which geodesics lie on projective lines.
Externí odkaz:
http://arxiv.org/abs/1301.2524
Autor:
Yu, Changtao
In this paper we study a class of Finsler metrics defined by a Riemannian metric and an 1-form. We classify those of projectively flat in dimension $n\geq3$ by a special class of deformations. The results show that the projective flatness of such kin
Externí odkaz:
http://arxiv.org/abs/1209.0845
Autor:
J. C. Álvarez Paiva, J. Barbosa Gomes
Publikováno v:
Journal of Topology and Analysis. :1-20
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
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f7e9a2ee72a09b999ee4d7ffa11df7dc
https://doi.org/10.1142/s1793525321500552
https://doi.org/10.1142/s1793525321500552
Autor:
Tabachnikov, Serge
We interpret magnetic billiards as Finsler ones and describe an analog of the string construction for magnetic billiards. Finsler billiards for which the law "angle of incidence equals angle of reflection" are described. We characterize the Finsler m
Externí odkaz:
http://arxiv.org/abs/math/0302288
Autor:
Alexey Stakhov, Samuil Aranson
Publikováno v:
British Journal of Mathematics & Computer Science. 12:1-25
Hilbert’s Fourth Problem is one of the most important mathema tical problems, formulated by Hilbert in 1900. Unfortunately, attempts to solve this problem during 20 th century did not lead to the generally recognized solution, and now modern mathem
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::40f6097ee0d409e1bc69d7b3d6b238ea
https://doi.org/10.9734/bjmcs/2016/21849
https://doi.org/10.9734/bjmcs/2016/21849