## Higher order geometries

The higher order geometrical structures
appear
in a natural way as plrongations of Riemannian and Finslerian
structures
to the Jet bundle. The attempts of A. Kawaguchi and J. K. Singe to
define
Higher Order Finsler structures were not sustantiated because the
conditions
imposed on the matrical function impliy that the fundamental tensor is
singular.

Higher Order Geometries were introduced by Prof. Dr. R.
Miron (Al. I.
Cuza University, Iasi, Romania). In a joint work we have defined the
notion
of homogeneity on the fibres of the Jet bundle. The fundamental tensor
of
such a structure is not singular anymore.

Recommended
bibliography:

1. R. Miron, *The Geometry of Higher Order Lagrange Spaces.
Applications
in Mechanics and Physics, *
Kluwer
Acad. Publ, FTP, Vol. 82, 1997.

2. R. Miron, *The Geometry of
Higher
Order Finsler Spaces*,
Hadronic
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

Finsler geometry is "the geometry of
families
of convex sets in R^n, parametrized by a manifold"(H. Busseman). It is
also
sometimes described as being "just the Riemannian geometry without the
quadratic
restriction" (S. S. Chern).

## Links

American
Mathematical Society

History of Mathematics

Springer-Verlag

Hokkaido University

Tokyo Metropolitan University

Centre
national de la recherche scientifique (in French)

Mathematics e-Print Archive

Resources

## Peoples

Z. Shen

R. L. Bryant

D.Bao

Hans-Bert
Rademacher