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Some Finsler spaces with homogeneous geodesics
Author(s) -
Yan Zaili
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500326
Subject(s) - geodesic , homogeneous , mathematics , space (punctuation) , pure mathematics , homogeneous space , orbit (dynamics) , mathematical analysis , geometry , combinatorics , computer science , engineering , aerospace engineering , operating system
A geodesic in a homogeneous Finsler space ( G / H , F ) is called a homogeneous geodesic if it is an orbit of a one‐parameter subgroup of G . A homogeneous Finsler space ( G / H , F ) is called Finsler g.o. space if its all geodesics are homogeneous. Recently, the author studied Finsler g.o. spaces and generalized some geometric results on Riemannian g.o. spaces to the Finslerian setting. In the present paper, we investigate homogeneous geodesics in homogeneous ( α , β ) spaces, and obtain the sufficient and necessary condition for an ( α , β ) space to be a g.o. space. As an application, we get a series of new examples of Finsler g.o. spaces.