Geodesics with constraints on Heisenberg manifolds
This paper is mainly devoted to give a qualitative description of the solutions to Euler-Lagrange equations with nonholonomic constraints. The geometry of the Heisenberg manifold, which appears in a natural way in some applications concerning magnetic resonance, plays a relevant role. In particular, using the structure of the Heissenberg group, the authors characterize the solutions as geodesics for a certain metric. Furthermore, the analog of the Gauss formula for the Heisenberg group is also given.
scientific article; zbMATH DE number 2062000