Abstract
Recently M. Matsumoto [5] studied automorphism of a Finsler bundle, called left translation of the bundle in his paper, and investigated the conditions that an automorphism preserves a Finsler connection. In this note, suggested by M. Matsumoto [5], we also study the gauge transformations of Finsler bundles and Finsler vector bundles, and investigate their actions on Finsler connections. It must be noted that our present study is a special case of a general theory, since Finsler bundles or Finsler vector bundles are defined as special fiber bundles over the tangent bundle of the base manifold (cf. Kirkovits-Otsuji-Aikou [4], Otsuji [7]).
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
T.Aikou, Differential geometry of Finsler vector bundles, Rep. Fac. Sci. Kagoshima Univ., (Math. Phys. & Chem.), 25, 1–20, 1992.
R. Hermann, Yang-Mills, Kaluza-Klein and the Einstein Program, Math. Sci. Press, 1978.
Y. Ichijyo, Almost Finsler structures and almost symplectic structures on tangent bundles, Riv. Mat. Univ. Parma,940 14, 29–54, 1988.
M.Sz. Kirkovits, T. Otsuji and T. Aikou, A note on automorphisms of Finsler bundles to appear in Rep. Fac. Sci. Kagoshima Univ., 26, 1993.
M. Matsumoto, A left translation preserving a Finsler connection invariant, Publ. Math. Debrecen 38, 1–2, 77–82, 1991.
I. Mogi and M. Itoh, Differential Geometry and Gauge Theory, (in Japanese), Kyoritsu Shuppan, Tokyo, 1986.
T. Otsuiji, Finsler geometry and some remarks of its applications (in Japanese), Master Thesis, Kagoshima University, 1992.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Kirkovits, M.S., Otsuji, T., Aikou, T. (1996). Some Remarks on Automorphisms of Finsler Bundles. In: Antonelli, P.L., Miron, R. (eds) Lagrange and Finsler Geometry. Fundamental Theories of Physics, vol 76. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8650-4_8
Download citation
DOI: https://doi.org/10.1007/978-94-015-8650-4_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4656-7
Online ISBN: 978-94-015-8650-4
eBook Packages: Springer Book Archive