Nilpotent (3, 6) Sub-Riemannian Problem

  • Authors:

  • O. Myasnichenko

  • Affiliations:

  • Mathematical Department, Moscow Aviation Institute, Volokolamskoe sh. 4, Moscow 125080, Russia, and SISSA-ISAS, Via Beirut 2-4, Trieste 34014, Italy. E-mail: myasnich@myasn.mccme.ru

  • Venue:
  • Journal of Dynamical and Control Systems
  • Year:
  • 2002

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Abstract

In this paper we study the nilpotent (3, 6) sub-Riemannian problem. We describe the envelope of sub-Riemannian geodesics starting from a fixed point. We also describe the wave fronts propagating from the point. For general nilpotent (n,n(n + 1)/2) sub-Riemannian problem we formulate a conjecture about the form of the variety where geodesics starting from a fixed point lose optimality.