A SASAKIAN STRUCTURE ON THE INDICATRIX BUNDLE OF A FINSLER SPACE WITH THE CHERN-RUND CONNECTION

Shigeo Fueki (Japan) and Hiroshi Endo (Japan)

Received February 25, 2008

References:

[1] M. Anastasiei, A historical remark on the connections of Chern and Rund, Cont. Math. 196 (1996), 171-176. [2] M. Anastasiei, A framed f-structure on tangent manifold of a Finsler space, Analele Univ. Bucuresti, Mat. -Inf., 2000, pp. 3-9. [3] P. L. Antonelli, R. S. Ingarden and M. Matsumoto, The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, FTPH58, Kluwer Academic Publishers, 1993. [4] P. L. Antonelli and R. Miron, Lagrange and Finsler Geometry Applications to Physics and Biology, Kluwer Press, 1996. [5] D. Bao, S. S. Chern and Z. Shen, An Introduction to Riemann-Finsler Geometry, Graduate Text in Mathematics, Vol. 200, Springer-Verlag, New York, 2000. [6] S. S. Chern, W. H. Chen and K. S. Lam, Lectures on Differential Geometry, Series on University Mathematics, Vol. 1, World Sci., 2000. [7] M. Matsumoto, Foundations of Finsler Geometry and Special Finsler Spaces, Kaiseisha Press, Japan, 1986. [8] R. Miron and M. Anastasiei, Vector Bundles and Lagrange Spaces with Applications to Relativity, Geometry Balkan Press, 1996. [9] H. Rund, The Differential Geometry of Finsler Spaces, Springer-Verlag, 1959. [10] K. Yano and M. Kon, Structures on Manifolds, World Scientific, 1984.

Keywords and phrases: Finsler manifold (space), indicatrix bundle, Chern-Rund connection, framed f-structure, Sasaki type metric.