Lagrange geometry on tangent manifolds
Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a nondegenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization which consi...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203303059 |
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| Summary: | Lagrange geometry is the geometry of the tensor field defined by
the fiberwise Hessian of a nondegenerate Lagrangian function on
the total space of a tangent bundle. Finsler geometry is the
geometrically most interesting case of Lagrange geometry. In this
paper, we study a generalization which consists of replacing the
tangent bundle by a general tangent manifold, and the Lagrangian
by a family of compatible, local, Lagrangian functions. We give
several examples and find the cohomological obstructions to
globalization. Then, we extend the connections used in Finsler
and Lagrange geometry, while giving an index-free presentation of
these connections. |
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| ISSN: | 0161-1712 1687-0425 |