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Almost Paracontact Structures and Time Dependent Lagrangians

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Abstract (2. Language): 
Let M be a smooth manifold and TM its tangent bundle. We associate to a nonlinear connection in the vector bundle £ • ^ x TM -» SR x M an ^^g^ paracontact structure on ^ x TM _ ^ js well-known ([1],[3]) that any regular time dependent Lagrangian -L'^x TM —> SR defines a nonlinear connection in the vector bundle , an almost paracontact structure depending on L is obtained. Several properties of it are pointed out.
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REFERENCES

References: 

1. Anastasiei M. - The Geometry of Time-Dependent Lagrangians, Math. Comput. Modelling, Vol. 20, no. 4/5, pp 67-81, 1994
2. Mihai I., Ro§ca R., Verstraelen L. - Some Aspects of the Differential GeomeUy of Vector Fields, PADGE, Vol. 2, 1996
3. Miron R., Anastasiei M. - The Geometry of Lagrange Spaces. Theoiy and Applications, Kluwer Academic Publishers, FTPH 59, 1994

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