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Geodesically reversible Finsler 2-spheres of constant curvature

dc.contributor.author Bryant, R
dc.contributor.editor Griffiths, Phillip A
dc.date.accessioned 2016-08-25T13:57:35Z
dc.date.issued 2006
dc.identifier.uri https://hdl.handle.net/10161/12683
dc.description.abstract A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodesically reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily projectively flat. As a corollary, using a previous result of the author, it is shown that a reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily a Riemannian metric of constant Gauss curvature, thus settling a long- standing problem in Finsler geometry.
dc.publisher World Scientific Publishers
dc.relation.ispartof Inspired by S. S. Chern---A Memorial Volume in Honor of a Great Mathematician
dc.relation.ispartof Nankai Tracts in Mathematics
dc.subject Finsler
dc.subject constant curvature
dc.title Geodesically reversible Finsler 2-spheres of constant curvature
dc.type Book section
duke.contributor.id Bryant, R|0110365
pubs.begin-page 95
pubs.end-page 111
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Trinity College of Arts & Sciences
pubs.place-of-publication Hackensack, NJ
pubs.publication-status Published
pubs.volume 11
duke.contributor.orcid Bryant, R|0000-0002-4890-2471


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