New aspects on $CR$-structures of codimension 2 on hypersurfaces of Sasakian manifolds

Dana Smetanova

Address.
Department of Algebra and Geometry, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic

E-mail.
Dana.Smetanova@upol.cz

Abstract.
The aim of the paper is to announce some recent results concerning Hamiltonian theory. The case of second order Euler--Lagrange form non-affine in the second derivatives is studied. Its related second order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler--Lagrange equations are found.

AMSclassification. 35A15, 49N60, 58Z05.

Keywords. Euler--Lagrange equations, Hamiltonian systems, Hamilton extremals, Dedecker--Hamilton extremals, Hamilton equations, Lepagean equivalents.