Sub-Riemannian Geometry [Hardcover]

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. Gromovs notion of tangent space.- ? 7. Distance estimates and the metric tangent space.- ? 8. Why is the tangent space a group?.- References.- Carnot-Carath?odory 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-Carath?odory 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.