Note on classical notion of Lee form

TL;DR

This paper explores the classical Lee form equation for arbitrary forms, extending previous work from non-degenerate 2-forms to more general cases using linear algebra of exterior forms.

Contribution

It generalizes Lee's results to odd-forms and the broader case where the form is not necessarily non-degenerate, expanding the theoretical understanding of the Lee form equation.

Findings

Extended Lee's results to odd-forms.

Analyzed the equation using linear algebra of exterior forms.

Provided new insights into the structure of the Lee form equation.

Abstract

This note is devoted to partial study of recurrent equation $d\omega=\beta \wedge \omega$, based on linear algebra of exterior forms. Such equation was considered by Lee, for non-degenerate 2-form. In this note we approach general case, when $\omega$ is arbitrary. Particularly, we extend results obtained by Lee, on odd-forms.