Skip to main content Accesibility Help
×
×
Home

A Class of Finsler Metrics with Bounded Cartan Torsion

  • Xiaohuan Mo (a1) and Linfeng Zhou (a2)
Abstract

In this paper, we find a class of (α, β) metrics which have a bounded Cartan torsion. This class contains all Randers metrics. Furthermore, we give some applications and obtain two corollaries about curvature of this metrics.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      A Class of Finsler Metrics with Bounded Cartan Torsion
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      A Class of Finsler Metrics with Bounded Cartan Torsion
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      A Class of Finsler Metrics with Bounded Cartan Torsion
      Available formats
      ×
Copyright
References
Hide All
[1] Bao, D. and Chern, S. S., A note on the Gauss-Bonnet theorem for Finsler spaces. Ann. Math. 143(1996), no. 2, 233252. doi:10.2307/2118643
[2] Bao, D., Chern, S. S., and Shen, Z., An Introduction to Riemann-Finsler Geometry. Graduate Texts inh Mathematics 200, Springer-Verlag, New York, 2000.
[3] Bao, D., Robles, C., and Shen, Z., Zermelo navigation on Riemannian manifolds. J. Differential Geom. 66(2004), no. 3, 377435.
[4] Burago, D. and Ivanov, S., Isometric embeddings of Finsler manifolds. Algebra i Analiz 5(1993), no. 1, 179192 (in Russian); translation in St.Petersburg Math. J. 5(1994), no. 1, 159–169.
[5] Cartan, E., Les espaces de Finsler. Actualités Scientifiques et Industrielles, no. 79, Hermann, Paris, 1934.
[6] Chern, S. S. and Shen, Z., Riemann-Finsler Geometry. Nankai Tracts in Mathematics 6, World Scientific, Hackensack, NJ, 2005.
[7] Deicke, A., Über die Finsler-Räume mit Ai = 0, Arch. Math. 4(1953), 4551. doi:10.1007/BF01899750
[8] Finsler, P., Über Kurven und Flächen in allgemeinen Räumen. Verlag Birkhäuser, Basel, 1951.
[9] Ernic, K., A Guide to Maple. Springer, 1999.
[10] Mo, X. and Yang, C., The explicit construction of Finsler metrics with special curvature properties. Differential. Geom. Appl. 24(2006), no. 2, 119129. doi:10.1016/j.difgeo.2005.08.004
[11] Nash, J., The immedding problem for Riemannian manifolds. Ann. of Math. 63(1956), 2063. doi:10.2307/1969989
[12] Shen, Z., Differential Geometry of Spray and Finsler Spaces. Kluwer Academic Publishers, Dordrecht, 2001.
[13] Shen, Z., Finsler metrics with K = 0 and S = 0 . Canad. J. Math. 55(2003), no. 1, 112132.
[14] Shen, Z., On R-quadratic Finsler spaces. Publ. Math. Debrecen 58(2001), no. 1–2, 263274.
[15] Shen, Z., On Finsler geometry of submanifolds. Math. Ann. 311(1998), no. 3, 549576. doi:10.1007/s002080050200
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed