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Nonholonomic tangent spaces: intrinsic construction and rigid dimensions
Author(s):
A.
Agrachev;
A.
Marigo
Journal:
Electron. Res. Announc. Amer. Math. Soc.
9
(2003),
111-120.
MSC (2000):
Primary 58A30;
Secondary 58K50
Posted:
November 13, 2003
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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:
10.1090/S1079-6762-03-00118-5
PII:
S 1079-6762(03)00118-5
Keywords:
Nonholonomic system,
nilpotent approximation,
Carnot group
Received by editor(s):
March 25, 2003
Posted:
November 13, 2003
Communicated by:
Svetlana Katok
Copyright of article:
Copyright
2003,
American Mathematical Society
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