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On Gromov's theory of rigid transformation groups: a dual approach

Published online by Cambridge University Press:  01 June 2000

ABDELGHANI ZEGHIB
ABDELGHANI ZEGHIB
Affiliation:
CNRS, UMPA, École Normale Supérieure de Lyon, 46, allée d'Italie, 69364 Lyon cedex 07, France (e-mail: [email protected])
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Abstract

Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual approach, which consists of enriching a plane field, as this is often practised in control theory, by adding brackets of the vector fields tangent to it and, then, looking for singular solutions of the obtained distribution. We apply this to the isometry problem of rigid geometric structures.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 3 , June 2000 , pp. 935 - 946
Copyright
2000 Cambridge University Press

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