The notion of generalized PN manifold is a framework which allows one to get properties of first integrals of the associated bihamiltonian system: conditions of existence of a bi-abelian subalgebra obtained from the momentum map and characterization of such an algebra linked with the problem of separation of variables.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-12,
author = {Fernand Pelletier and Patrick Cabau},
title = {Generalized PN manifolds and separation of variables},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {163-181},
zbl = {1153.37395},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-12}
}
Fernand Pelletier; Patrick Cabau. Generalized PN manifolds and separation of variables. Banach Center Publications, Tome 83 (2008) pp. 163-181. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-12/