Bi-Legendrian connections
Volume 86 / 2005
Annales Polonici Mathematici 86 (2005), 79-95
MSC: 53C12, 53C15, 53B05, 57R30.
DOI: 10.4064/ap86-1-8
Abstract
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 $\mathbb{R}^{2n+r}$.
