Ahangari F. Geometric analysis of metric Legendre foliated cocycles on contact manifolds via SODE structure (abstract)

From Geometry of Differential Equations
Jump to navigation Jump to search

Speaker: Fatemeh Ahangari

Title: Geometric analysis of metric Legendre foliated cocycles on contact manifolds via SODE structure

Abstract:
In recent years, an increasing consideration has been devoted to the qualitative analysis of systems of (non-) autonomous second (higher) order ordinary (partial) differential equations fields through some associated geometric structures. Second order ordinary differential equations (SODE) are of special significance mainly due to their extensive applications in various domains of mathematics, science and engineering. A remarkably type of SODE is the one which can be deduced from a variational principle. In this research, a thoroughgoing structural investigation of the transverse Legendre foliated cocycles on contact manifolds is presented. For this goal, by applying Spencer theory of formal integrability, sufficient conditions for the metric associated with the given SODE structure are designated to extend to a transverse metric for the lifted Legendre foliated cocycle on the tangent space of an arbitrary contact manifold. Indeed, the concept of formal integrability is applied as a noteworthy reformulation of the inverse problem of the calculus of variations in terms of a partial differential operator which acts on semi-basic 1-forms. Consequently, this expression of the Helmholtz metrizability conditions, enables us to construct a transverse metric on the tangent bundle of a given contact manifold which leads to creation of the specific type of metric Legendre foliated cocycles which are entirely compatible with SODE structure.


Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.