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＜電子ブック＞
Sub-Riemannian Geometry / edited by Andre Bellaiche, Jean-Jaques Risler
(Progress in Mathematics. ISSN:2296505X ; 144)

版	1st ed. 1996.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	1996
本文言語	英語
大きさ	VIII, 398 p : online resource
著者標目	Bellaiche, Andre editor Risler, Jean-Jaques editor SpringerLink (Online service)
件　名	LCSH:Geometry, Differential LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) FREE:Differential Geometry FREE:Global Analysis and Analysis on Manifolds
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-0348-9210-0

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