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TitleSub-Riemannian Geometry [electronic resource] / edited by Andrรฉ Bellaรฏche, Jean-Jacques Risler
ImprintBasel : Birkhรคuser Basel, 1996
Connect tohttp://dx.doi.org/10.1007/978-3-0348-9210-0
Descript VIII, 398 p. online resource

CONTENT

The tangent space in sub-Riemannian geometry -- ยง 1. Sub-Riemannian manifolds -- ยง 2. Accessibility -- ยง 3. Two examples -- ยง 4. Privileged coordinates -- ยง 5. The tangent nilpotent Lie algebra and the algebraic structure of the tangent space -- ยง 6. Gromovโ{128}{153}s notion of tangent space -- ยง 7. Distance estimates and the metric tangent space -- ยง 8. Why is the tangent space a group? -- References -- Carnot-Carathรฉodory spaces seen from within -- ยง 0. Basic definitions, examples and problems -- ยง 1. Horizontal curves and small C-C balls -- ยง 2. Hypersurfaces in C-C spaces -- ยง 3. Carnot-Carathรฉodory geometry of contact manifolds -- ยง 4. Pfaffian geometry in the internal light -- ยง 5. Anisotropic connections -- References -- Survey of singular geodesics -- ยง 1. Introduction -- ยง 2. The example and its properties -- ยง 3. Some open questions -- ยง 4. Note in proof -- References -- A cornucopia of four-dimensional abnormal sub-Riemannian minimizers -- ยง 1. Introduction -- ยง 2. Sub-Riemannian manifolds and abnormal extremals -- ยง 3. Abnormal extremals in dimension 4 -- ยง 4. Optimality -- ยง 5. An optimality lemma -- ยง 6. End of the proof -- ยง 7. Strict abnormality -- ยง 8. Conclusion -- References -- Stabilization of controllable systems -- ยง 0. Introduction -- ยง 1. Local controllability -- ยง 2. Sufficient conditions for local stabilizability of locally controllable systems by means of stationary feedback laws -- ยง 3. Necessary conditions for local stabilizability by means of stationary feedback laws -- ยง 4. Stabilization by means of time-varying feedback laws -- ยง 5. Return method and controllability -- References


Mathematics Global analysis (Mathematics) Manifolds (Mathematics) Differential geometry Mathematics Differential Geometry Global Analysis and Analysis on Manifolds



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