A note on metric nonlinear connections on the cotangent bundle

In the present paper we continue the investigation of nonlinear connections started in [16]. The problem of metrizability of the nonlinear connection on the cotangent bundle is studied. Using the dynamical covariant derivative induced by a regular vector field, we find the coefficients of a metric nonlinear connection. For the particular case of a Hamiltonian space we prove that the canonical nonlinear connection is a unique metric and symmetric nonlinear connection.