Metric nonlinear connections on Lie algebroids
نویسنده
چکیده
In this paper the problem of compatibility between a nonlinear connection and other geometric structures on Lie algebroids is studied. The notion of dynamical covariant derivative is introduced and a metric nonlinear connection is found in the more general case of Lie algebroids. We prove that the canonical nonlinear connection induced by a regular Lagrangian on a Lie algebroid is the unique connection which is metric and compatible with the symplectic structure. M.S.C. 2010: 53C05, 17B66, 70S05.
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