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Nonholonomic tangent spaces: intrinsic construction and rigid dimensions


Authors: A. Agrachev and A. Marigo
Journal: Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 111-120
MSC (2000): Primary 58A30; Secondary 58K50
Published electronically: November 13, 2003
MathSciNet review: 2029472
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.


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Additional Information

A. Agrachev
Affiliation: Steklov Mathematical Institute, Moscow, Russia
Address at time of publication: SISSA, Via Beirut 2–4, Trieste, Italy
Email: agrachev@ma.sissa.it

A. Marigo
Affiliation: IAC-CNR, Viale Policlinico 136, Roma, Italy
Email: marigo@iac.rm.cnr.it

DOI: http://dx.doi.org/10.1090/S1079-6762-03-00118-5
Keywords: Nonholonomic system, nilpotent approximation, Carnot group
Received by editor(s): March 25, 2003
Published electronically: November 13, 2003
Communicated by: Svetlana Katok
Article copyright: © Copyright 2003 American Mathematical Society