Bi-Legendrian connections

Beniamino Cappelletti Montano¹

¹ Department of Mathematics University of Bari via E. Orabona, 4 70125 Bari, Italy

Annales Polonici Mathematici, Tome 86 (2005) no. 1, pp. 79-95.

Résumé

We define the concept of a bi-Legendrian connection associated to a bi-Legendrian structure on an almost $\cal{S}$-manifold $M^{2n+r}$. 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 $\mathbb{R}^{2n+r}$.

Détail

DOI : 10.4064/ap86-1-8

Keywords: define concept bi legendrian connection associated bi legendrian structure almost cal manifold among other things compute torsion connection prove curvature vanishes along leaves bi legendrian structure moreover prove bi legendrian connection flat bi legendrian structure locally equivalent standard structure mathbb