Journal of Dynamical and Control Systems
We show that strictly abnormal geodesics arise in graded nilpotent Lie groups. We construct a group, with a left invariant bracket-generating distribution, for which some Carnot geodecics are strictly abnormal and, in fact, not normal in any subgroup. In the 2-step case we also prove that these geodesics are always smooth. Our main technique is based on the equations for the normal and abnormal curves, which we derive (for any Lie group) explicitly in terms of the structure constants. © 1995 Plenum Publishing Corporation.
1991 Mathematics Subject Classification: 53C20, 53C21, 53C22, abnormal geodesics, nilpotent Lie group, Sub-Riemannian geometry
© the authors
Golé, Christophe and Karidi, Ron, "A Note on Carnot Geodesics in Nilpotent Lie Groups" (1995). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.