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A nonholonomic space is a smooth manifold equipped with a bracket generating family of vector fields. Its infinitesimal version is a homogeneous space of a nilpotent Lie group endowed with a dilation which measures the anisotropy of the space. We give an intrinsic construction of these infinitesimal objects and classify all rigid (i.e. not deformable) cases.

Copyright 2003 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 09 (2003), pp. 111-120
• Publisher Identifier: S 1079-6762(03)00118-5
• 2000 Mathematics Subject Classification. Primary 58A30; Secondary 58K50
• Key words and phrases. Nonholonomic system, nilpotent approximation, Carnot group
• Received by editors March 25, 2003
• Posted on November 13, 2003
• Communicated by Svetlana Katok
• Comments (When Available)

A. Agrachev

Steklov Mathematical Institute, Moscow, Russia

Current address: SISSA, Via Beirut 2--4, Trieste, Italy

E-mail address: agrachev@ma.sissa.it

A. Marigo

IAC-CNR, Viale Policlinico 136, Roma, Italy

E-mail address: marigo@iac.rm.cnr.it