arXiv Analytics

Sign in

arXiv:1209.0845 [math.DG]AbstractReferencesReviewsResources

Deformations and Hilbert's Fourth Problem

Changtao Yu

Published 2012-09-05Version 1

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 kind of Finsler metrics always arises from that of some Riemannian metric.

Comments: 26 pages, 1 figure
Categories: math.DG, math.MG
Subjects: 53B40, 53C60
Related articles: Most relevant | Search more
arXiv:1209.0857 [math.DG] (Published 2012-09-05)
On a new class of Finsler metrics
arXiv:2204.05678 [math.DG] (Published 2022-04-12)
First integrals for Finsler metrics with vanishing $χ$-curvature
arXiv:1401.0061 [math.DG] (Published 2013-12-31, updated 2015-02-04)
On dually flat general $(α,β)$-metrics

Links

Toolbox