A zoo of coisotropic embeddings

Abstract

The aim of this paper is to extend the coisotropic embedding theorem obtained by M. J. Gotay for pre-symplectic manifolds to more general geometric settings: cosymplectic, contact, cocontact, $k$-symplectic, $k$-cosymplectic, $k$-contact, and multisymplectic manifolds. The results are obtained by applying a generic methodology, which gives more relevance to the potential applications. In that sense, this paper gives the fundamental basis to be able to apply the results to the so-called regularization problem of singular Lagrangian systems, both in mechanics and in classical field theories.