Sub-Riemannian Geometry (Progress in Mathematics, Band 144) - Softcover

Softcover

ISBN 10: 3034899467 ISBN 13: 9783034899468

Verlag: Birkhäuser, 2011

Inhaltsangabe

The tangent space in sub-Riemannian geometry.- § 1. Sub-Riemannian manifolds.- § 2. Accessibility.- § 3. Two examples.- § 4. Privileged coordinates.- § 5. The tangent nilpotent Lie algebra and the algebraic structure of the tangent space.- § 6. Gromov's notion of tangent space.- § 7. Distance estimates and the metric tangent space.- § 8. Why is the tangent space a group?.- References.- Carnot-Carathéodory spaces seen from within.- § 0. Basic definitions, examples and problems.- § 1. Horizontal curves and small C-C balls.- § 2. Hypersurfaces in C-C spaces.- § 3. Carnot-Carathéodory geometry of contact manifolds.- § 4. Pfaffian geometry in the internal light.- § 5. Anisotropic connections.- References.- Survey of singular geodesics.- § 1. Introduction.- § 2. The example and its properties.- § 3. Some open questions.- § 4. Note in proof.- References.- A cornucopia of four-dimensional abnormal sub-Riemannian minimizers.- § 1. Introduction.- § 2. Sub-Riemannian manifolds and abnormal extremals.- § 3. Abnormal extremals in dimension 4.- § 4. Optimality.- § 5. An optimality lemma.- § 6. End of the proof.- § 7. Strict abnormality.- § 8. Conclusion.- References.- Stabilization of controllable systems.- § 0. Introduction.- § 1. Local controllability.- § 2. Sufficient conditions for local stabilizability of locally controllable systems by means of stationary feedback laws.- § 3. Necessary conditions for local stabilizability by means of stationary feedback laws.- § 4. Stabilization by means of time-varying feedback laws.- § 5. Return method and controllability.- References.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2011
• Sprache: Englisch
• ISBN 10: 3034899467
• ISBN 13: 9783034899468
• Einband: Taschenbuch
• Anzahl der Seiten: 408
• Herausgeber: Bellaiche Andre, Risler Jean-Jaques
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland