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Autori: Popescu, Liviu
Editorial: Balkan Journal of Geometry and its Applications, vol. 16, no. 1, p.111-121, 2011.
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.
Cuvinte cheie: metric nonlinear connection, Lie algebroids