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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832558230586261504 |
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| author | Izu Vaisman |
| author_facet | Izu Vaisman |
| author_sort | Izu Vaisman |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-269d69974da043b2a2a6531d1a785f37 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-269d69974da043b2a2a6531d1a785f372025-02-03T01:32:51ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003513241326610.1155/S0161171203303059Lagrange geometry on tangent manifoldsIzu Vaisman0Department of Mathematics, University of Haifa, Haifa 31905, IsraelLagrange 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.http://dx.doi.org/10.1155/S0161171203303059 |
| spellingShingle | Izu Vaisman Lagrange geometry on tangent manifolds International Journal of Mathematics and Mathematical Sciences |
| title | Lagrange geometry on tangent manifolds |
| title_full | Lagrange geometry on tangent manifolds |
| title_fullStr | Lagrange geometry on tangent manifolds |
| title_full_unstemmed | Lagrange geometry on tangent manifolds |
| title_short | Lagrange geometry on tangent manifolds |
| title_sort | lagrange geometry on tangent manifolds |
| url | http://dx.doi.org/10.1155/S0161171203303059 |
| work_keys_str_mv | AT izuvaisman lagrangegeometryontangentmanifolds |