Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
ELECTRONIC RESEARCH ANNOUNCEMENTS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: ELECTRONIC RESEARCH ANNOUNCEMENTS
OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 00, Pages 000--000 (Xxxx XX, XXXX)
S 1079­6762(XX)0000­0
NONHOLONOMIC TANGENT SPACES: INTRINSIC
CONSTRUCTION AND RIGID DIMENSIONS
A. AGRACHEV AND A. MARIGO
Abstract. A nonholonomic space is a smooth manifold equipped with a
bracket generating family of vector fields. Its infinitesimal version is a ho­
mogeneous space of a nilpotent Lie group endowed with a dilation which mea­
sures the anisotropy of the space. We give the intrinsic construction of these
infinitesimal objects and classify all rigid (i.e. not deformable) cases.
1. Introduction
Let M be a (C # ­) smooth connected n­dimensional manifold and F # VecM
be a set of smooth vector fields on M . Given q # M and an integer l > 0 we set
# l
q = span{[f 1 , [· · · , [f i-1 , f i ] · · · ](q) : f j # F , 1 # j # i, i # l} # T q M.
Of course, # l
q # # m
q for l < m. The set F is called bracket generating (or com­

  

Source: Agrachev, Andrei - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)

 

Collections: Engineering; Mathematics