Higher order geometries
The higher order geometrical structures
in a natural way as plrongations of Riemannian and Finslerian
to the Jet bundle. The attempts of A. Kawaguchi and J. K. Singe to
Higher Order Finsler structures were not sustantiated because the
imposed on the matrical function impliy that the fundamental tensor is
Higher Order Geometries were introduced by Prof. Dr. R.
Miron (Al. I.
Cuza University, Iasi, Romania). In a joint work we have defined the
of homogeneity on the fibres of the Jet bundle. The fundamental tensor
such a structure is not singular anymore.
1. R. Miron, The Geometry of Higher Order Lagrange Spaces.
in Mechanics and Physics,
Acad. Publ, FTP, Vol. 82, 1997.
2. R. Miron, The Geometry of
Order Finsler Spaces,
Press, USA, 1998.
3 . R. Miron, D. Hrimiuc, H. Shimada, S. V. Sabau, The Geometry of
Lagrange and Hamilton Spaces, Kluwer Acad. Publ, FTP, Vol. 118, 2001.
Finsler geometry is "the geometry of
of convex sets in R^n, parametrized by a manifold"(H. Busseman). It is
sometimes described as being "just the Riemannian geometry without the
restriction" (S. S. Chern).
History of Mathematics
Tokyo Metropolitan University
national de la recherche scientifique (in French)
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R. L. Bryant