Shortest paths for sub-Riemannian metrics on rank-two distributions /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Liu, Wensheng, 1962- (Autor), Sussmann, Hector J., 1946- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island, United States : American Mathematical Society, 1995.
Colección:Memoirs of the American Mathematical Society ; Volume 118, no. 564.
Temas:
Geometry, Riemannian.
Geodesics (Mathematics)
Géométrie de Riemann.
Géodésiques (Mathématiques)
Geometry, Riemannian
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Table of Contents
  • 1 Introduction
  • 2 Three examples
  • 2.1 Riemannian geodesies
  • 2.2 The Heisenberg algebra case
  • 2.3 An abnormal minimizer
  • 3 Notational conventions and definitions
  • 3.1 Manifolds, charts, bundles, curves and arcs
  • 3.2 Hamiltonian functions, Hamilton vector fields, and bicharacteristics
  • 3.3 Hamiltonian lifts and characteristics
  • 3.4 Distributions, admissible curves, orbits
  • 3.5 Nonholonomic distributions; regularity
  • 4 Abnormal extremals
  • 5 Sub-Riemannian manifolds, length minimizers and extremals
  • 5.1 The sub-Riemannian distance, length minimization and time optimality5.2 Extremals
  • 5.3 The relationship between minimality and extremality
  • 6 Regular abnormal extremals for rank-two distributions
  • 6.1 The regular abnormal foliation of a rank-two distribution
  • 6.2 Regular abnormal biextremals of a sub-Riemannian manifold
  • 7 Local optimality of regular abnormal extremals
  • 7.1 The main inequality
  • 7.2 The normal form theorem
  • 7.3 The optimality theorem
  • 8 Strict abnormality
  • 9 Some special cases
  • 9.1 2- and 3-generating distributions
  • 9.2 3-Regular distributions9.3 The 4- and 5-dimensional cases
  • 9.4 The three-dimensional case
  • 9.5 A Lie group example
  • 9.6 A nonsmooth abnormal extremal
  • Appendix A: The Gaveau-Brockett problem
  • Appendix B: Proof of Theorem 1
  • B.l: Control systems
  • B.2: The Maximum Principle
  • Appendix C: Local optimality of normal extremals
  • Appendix D: Rigid sub-Riemannian arcs and local optimality
  • Appendix E: A nonoptimality proof
  • References

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