A Note on Carnot Geodesics in Nilpotent Lie Groups

Authors

Christophe Golé, Smith CollegeFollow
Ron Karidi, Stanford University

Document Type

Article

Publication Date

10-1-1995

Publication Title

Journal of Dynamical and Control Systems

Abstract

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.

Keywords

1991 Mathematics Subject Classification: 53C20, 53C21, 53C22, abnormal geodesics, nilpotent Lie group, Sub-Riemannian geometry

Volume

1

Issue

4

First Page

535

Last Page

549

DOI

10.1007/BF02255895

ISSN

10792724

Rights

© the authors

Comments

Author’s submitted manuscript.

Recommended Citation

Golé, Christophe and Karidi, Ron, "A Note on Carnot Geodesics in Nilpotent Lie Groups" (1995). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/82