Bi-Legendrian connections

CAPPELLETTI MONTANO, BENIAMINO

2005-01-01

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Abstract

We define the concept of a bi-Legendrian connection associated to a bi- Legendrian structure on an almost 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 R^{2n+r}.