Items related to Sub-Riemannian Geometry: 144 (Progress in Mathematics,...
Synopsis
Sub-Riemannian geometry (also known as Carnot geometry in France, and non-holonomic Riemannian geometry in Russia) has been a full research domain for fifteen years, with motivations and ramifications in several parts of pure and applied mathematics, namely: • control theory • classical mechanics • Riemannian geometry (of which sub-Riemannian geometry constitutes a natural generalization, and where sub-Riemannian metrics may appear as limit cases) • diffusion on manifolds • analysis of hypoelliptic operators • Cauchy-Riemann (or CR) geometry. Although links between these domains had been foreseen by many authors in the past, it is only in recent years that sub- Riemannian geometry has been recognized as a possible common framework for all these topics. This book provides an introduction to sub-Riemannian geometry and presents the state of the art and open problems in the field. It consists of five coherent and original articles by the leading specialists: • André Bellaïche: The tangent space in sub-Riemannian geometry • Mikhael Gromov: Carnot-Carathéodory spaces seen from within • Richard Montgomery: Survey of singular geodesics • Héctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers • Jean-Michel Coron: Stabilization of controllable systems
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Synopsis
This work provides an introduction to sub-Riemannian geometry and presents up-to-date problems in the field.
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Sub-Riemannian Geometry (Progress in Mathematics, 144)
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Sub-Riemannian Geometry
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Sub-Riemannian Geometry
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Condition: New. Sub-Riemannian geometry has been a full research domain, with motivations and ramifications in several parts of pure and applied mathematics. This book provides an introduction to sub-Riemannian geometry. Editor(s): Bass, Hyman; Risler, Jean-Jaques. Series: Progress in Mathematics. Num Pages: 398 pages, biography. BIC Classification: PBMP. Category: (P) Professional & Vocational. Dimension: 235 x 155 x 23. Weight in Grams: 752. . 1996. 1996th Edition. hardcover. . . . . Seller Inventory # V9783764354763
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Sub-Riemannian Geometry (Progress in Mathematics, 144, Band 144)
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Sub-Riemannian Geometry.
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Sub-Riemannian Geometry (Progress in Mathematics, 144)
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Sub-Riemannian Geometry
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Condition: New. Sub-Riemannian geometry has been a full research domain, with motivations and ramifications in several parts of pure and applied mathematics. This book provides an introduction to sub-Riemannian geometry. Editor(s): Bass, Hyman; Risler, Jean-Jaques. Series: Progress in Mathematics. Num Pages: 398 pages, biography. BIC Classification: PBMP. Category: (P) Professional & Vocational. Dimension: 235 x 155 x 23. Weight in Grams: 752. . 1996. 1996th Edition. hardcover. . . . . Books ship from the US and Ireland. Seller Inventory # V9783764354763
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Sub-Riemannian Geometry
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783764354763