Recursion Operator in a Noncommutative Minkowski Phase Space

@article{Hounkonnou2019RecursionOI,
  title={Recursion Operator in a Noncommutative Minkowski Phase Space},
  author={Mahouton Norbert Hounkonnou and Mahougnon Justin Landalidji and E. Baloitcha},
  journal={Trends in Mathematics},
  year={2019}
}
A recursion operator for a geodesic flow, in a noncommutative (NC) phase space endowed with a Minkowski metric, is constructed and discussed in this work. A NC Hamiltonian function \({\mathcal{H}}_{\mathrm{nc}}\) describing the dynamics of a free particle system in such a phase space, equipped with a noncommutative symplectic form ωnc is defined. A related NC Poisson bracket is obtained. This permits to construct the NC Hamiltonian vector field, also called NC geodesic flow. Further, using a… 
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