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June  2010, 2(2): 199-221. doi: 10.3934/jgm.2010.2.199

Regularity of generating families of functions

Włodzimierz M. Tulczyjew 1, and  Paweł Urbański 2,

1. 

Valle San Benedetto, 2, 62030 Monte Cavallo, Italy
2. 

Division of Mathematical Methods in Physics, University of Warsaw, Hoża 74, 00-682 Warszawa, Poland

Received  February 2010 Revised  June 2010 Published  June 2010

We describe the geometric structures involved in the variational formulation of physical theories. In presence of these structures, the constitutive set of a physical system can be generated by a family of functions. We discuss conditions, under which a family of functions generates an immersed Lagrangian submanifold. These conditions are given in terms of the Hessian of the family.
Keywords: Lagrangian submanifold, Liouville structure, Hessian., symplectic reduction.
Mathematics Subject Classification: Primary: 53D12, 70G75; Secondary: 70H99, 49S0.
Citation: Włodzimierz M. Tulczyjew, Paweł Urbański. Regularity of generating families of functions. Journal of Geometric Mechanics, 2010, 2 (2) : 199-221. doi: 10.3934/jgm.2010.2.199
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