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Nonholonomic tangent spaces: intrinsic construction and rigid dimensions
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Nonholonomic tangent spaces: intrinsic construction and rigid dimensions
A. Agrachev, A. Marigo
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.
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
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