Projectively flat Finsler 2-spheres of constant curvature

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 1997Embargo end date: 01 Nov 1996 United States English Publisher:Springer Science and Business Media LLCJournal:Selecta Mathematica, volume 3, pages 161-203 (issn: 1022-1824, eissn: 1420-9020,

Copyright policy )Funded by:NSF | Mathematical Sciences: Th...

Authors: Bryant, RL;

doi: 10.1007/s000290050009 , 10.48550/arxiv.dg-ga/9611010

arXiv: dg-ga/9611010

handle: 10161/13152

Projectively flat Finsler 2-spheres of constant curvature

- Summary
- Subjects
- Metrics

Abstract

I classify the Finsler structures on the 2-sphere that have constant Finsler-Gauss curvature and whose geodesics are the great circles. Modulo diffeomorphism, there is a 2-parameter family of such Finsler structures, only one of which is homogeneous or symmetric, namely the Riemannian one. I discuss the history of the problem and its relation with Hilbert's Fourth Problem and the calculus of variations.

AMS-TeX v2.1, amsppt.sty (v. 2.1d), 38 pages

Country

United States

Related Organizations

Duke University
United States

Keywords

Mathematics - Differential Geometry, Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.), 53C60 (Primary) 53A20 (Secondary), Projective differential geometry, projective geometry, Global differential geometry of Finsler spaces and generalizations (areal metrics), Differential Geometry (math.DG), FOS: Mathematics, geodesic path geometry, Finsler geometry

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	62
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 1%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average