Invariant formulation of a variational problem

TL;DR

This paper develops a Hamiltonian framework for invariant variational problems on submanifolds, extending multisymplectic methods to a broader geometric setting.

Contribution

It introduces an invariant Hamiltonian formulation for variational problems on submanifolds, generalizing multisymplectic approaches.

Findings

Provides a new geometric Hamiltonian formulation for invariant variational problems.

Extends multisymplectic theory to submanifolds of arbitrary dimension.

Lays groundwork for further geometric analysis of variational problems.

Abstract

In this paper we present a Hamiltonian formulation of multisymplectic type of an invariant variational problem on smooth submanifold of dimension $p$ in a smooth manifold of dimension $n$ with $p<n$.