We define the concept of a bi-Legendrian connection associated to a bi-Legendrian structure on an almost -manifold . Among other things, we compute the torsion of this connection and prove that the curvature vanishes along the leaves of the bi-Legendrian structure. Moreover, we prove that if the bi-Legendrian connection is flat, then the bi-Legendrian structure is locally equivalent to the standard structure on .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-1-8,
author = {Beniamino Cappelletti Montano},
title = {Bi-Legendrian connections},
journal = {Annales Polonici Mathematici},
volume = {85},
year = {2005},
pages = {79-95},
zbl = {1081.53028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-1-8}
}
Beniamino Cappelletti Montano. Bi-Legendrian connections. Annales Polonici Mathematici, Tome 85 (2005) pp. 79-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-1-8/