Abstract.
In this paper, we introduce a new understanding tool, the Finsler hyperbolic geometric flow, and establish the short-time existence and uniqueness theorem for reduced Berwald spaces. This kind of flow is very natural to understand certain wave phenomena in physics as well as the geometry of Finsler manifolds. Also we illustrate the wave character of the metrics and curvatures of reduced Berwald manifolds.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.X. Kong, K. Liu, J. Math. Phys. 48, 103508-1 (2007)
S. Azami, A. Razavi, Int. J. Geom. Methods Mod. Phys. 10, 1250091-1 (2013)
P.L. Antonelli, T.J. Zastawniak, Fundamentals of Finslerian Diffusion with Applications, Vol. 101 (Springer Netherlands, 1999)
W.R. Dai, D.X. Kong, K. Liu, Pure Appl. Math. Quart. 6, 331 (2010)
F. John, Proc. Natl. Acad. Sci. U.S.A. 73, 281 (1976)
S. Klainerman, Commun. Pure Appl. Math. 33, 41 (1980)
D. Bao, C. Robles, Ricci and flag curvatures in Finsler geometry in A Sampler of Riemann-Finsler Geometry, Vol. 50 edited by D. Bao, R.L. Bryant, S.S. Chern, Z. Shen (MSRI Publications, 2004) pp. 197--259
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Aral, Z., Razavi, A. Hyperbolic geometric flow on reduced Berwald spaces: Short-time existence and uniqueness. Eur. Phys. J. Plus 132, 310 (2017). https://doi.org/10.1140/epjp/i2017-11592-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2017-11592-7