Density-valued symplectic forms from a multisymplectic viewpoint

TL;DR

This paper characterizes a special class of multisymplectic manifolds with density-valued symplectic forms, establishes Darboux-type theorems for them, and explores their symmetries from a multisymplectic perspective.

Contribution

It provides an intrinsic characterization and Darboux-type theorems for density-valued symplectic forms in multisymplectic manifolds, advancing understanding of their geometric structure.

Findings

Intrinsic characterization of density-valued symplectic forms

Darboux-type theorems for these forms

Analysis of their symmetries

Abstract

We give an intrinsic characterization of multisymplectic manifolds that have the linear type of density-valued symplectic forms in each tangent space, prove Darboux-type theorems for these forms, and investigate their symmetries.