Abstract
Some years ago Moshé Flato pointed out that it would be interesting to develop Nambu's idea to generalize Hamiltonian mechanics. An interesting new formalism in that direction was proposed by L. Takhtajan. His theory gave new perspectives concerning deformation quantization, and many authors have developed its mathematical features. The purpose of this Letter is to show that this theory, at first dedicated to physics, presents a new point of view for the study of singularities of integrable 1-forms. Namely, we will prove that any integrable 1-form which vanishes at a point and has a nonzero linear part at this point is, up to multiplication by a nonvanishing function, the formal pull-back of a two-dimensional 1-form. We also obtain a classification of quadratic integrable 1-forms.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.