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Sub-Riemannian Geometry, Andre Bellaiche; Jean-Jaques Risler


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Автор: Andre Bellaiche; Jean-Jaques Risler
Название:  Sub-Riemannian Geometry
ISBN: 9783034899468
Издательство: Springer
Классификация:



ISBN-10: 3034899467
Обложка/Формат: Paperback
Страницы: 398
Вес: 0.57 кг.
Дата издания: 18.10.2011
Серия: Progress in Mathematics
Язык: English
Размер: 234 x 156 x 21
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание:

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:
- Andre Bellaiche: The tangent space in sub-Riemannian geometry - Mikhael Gromov: Carnot-Caratheodory spaces seen from within - Richard Montgomery: Survey of singular geodesics - Hector J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers - Jean-Michel Coron: Stabilization of controllable systems




Variational Problems in Riemannian Geometry

Автор: Paul Baird; Ahmad El Soufi; Ali Fardoun; Rachid Re
Название: Variational Problems in Riemannian Geometry
ISBN: 3034896409 ISBN-13(EAN): 9783034896405
Издательство: Springer
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Цена: 13974.00 р.
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Описание: This volume has grown from a conference entitled Harmonic Maps, Minimal Sur- faces and Geometric Flows which was held at the Universite de Bretagne Occi- dentale from July 7th-12th, 2002, in the town of Brest in Brittany, France. We welcomed many distinguished mathematicians from around the world and a dy- namic meeting took place, with many fruitful exchanges of ideas. In order to produce a work that would have lasting value to the mathematical community, the organisers decided to invite a small number of participants to write in-depth articles around a common theme. These articles provide a balance between introductory surveys and ones that present the newest results that lie at the frontiers of research. We thank these mathematicians, all experts in their field, for their contributions. Such meetings depend on the support of national organisations and the local community and we would like to thank the following: the Ministere de l'Education Nationale, Ministere des Affaires Etrangeres, Centre National de Recherche Sci en- tifique (CNRS), Conseil Regional de Bretagne, Conseil General du Finistere, Com- munaute Urbaine de Brest, Universite de Bretagne Occidentale (UBO), Faculte des Sciences de l'UBO, Laboratoire de Mathematiques de l'UBO and the Departement de Mathematiques de l'UBO. Their support was generous and ensured the success of the meeting. We would also like to thank the members of the scientific committee for their advice and for their participation in the conception and composition of this volume: Pierre Berard, Jean-Pierre Bourguignon, Frederic Helein, Seiki Nishikawa and Franz Pedit.

Geometric Control Theory and Sub-Riemannian Geometry

Автор: Gianna Stefani; Ugo Boscain; Jean-Paul Gauthier; A
Название: Geometric Control Theory and Sub-Riemannian Geometry
ISBN: 3319350250 ISBN-13(EAN): 9783319350257
Издательство: Springer
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Цена: 15372.00 р.
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Описание: Presenting state-of-the-art research in a highly applicable field, this collection features papers by leading scientists combining these two methodologies, in honor of the groundbreaking work of Andrei Agrachev. It includes a chapter on open problems.

Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning

Автор: Fr?d?ric Jean
Название: Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning
ISBN: 3319086898 ISBN-13(EAN): 9783319086897
Издательство: Springer
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Цена: 6986.00 р.
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Описание: Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems.

Geometric Control Theory and Sub-Riemannian Geometry

Автор: Gianna Stefani; Ugo Boscain; Jean-Paul Gauthier; A
Название: Geometric Control Theory and Sub-Riemannian Geometry
ISBN: 3319021311 ISBN-13(EAN): 9783319021317
Издательство: Springer
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Цена: 13974.00 р.
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Описание: Presenting state-of-the-art research in a highly applicable field, this collection features papers by leading scientists combining these two methodologies, in honor of the groundbreaking work of Andrei Agrachev. It includes a chapter on open problems.

Singular Semi-Riemannian Geometry

Автор: D.N. Kupeli
Название: Singular Semi-Riemannian Geometry
ISBN: 0792339967 ISBN-13(EAN): 9780792339960
Издательство: Springer
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Цена: 10760.00 р.
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Описание: Provides an exposition of singular semi-Riemannian geometry, the study of a smooth manifold furnished with a degenerate (singular) metric tensor of arbitrary signature. This book is intended for graduate students of differential geometry, who have some background knowledge on the subject of complex manifolds.

Pseudo-Riemannian Geometry, Delta-Invariants And Applications

Автор: Chen Bang-Yen
Название: Pseudo-Riemannian Geometry, Delta-Invariants And Applications
ISBN: 9814329630 ISBN-13(EAN): 9789814329637
Издательство: World Scientific Publishing
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Цена: 25344.00 р.
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Описание: Provides an introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. In this book, a number of results on pseudo-Riemannian submanifolds are also included.

Riemannian Submersions, Riemannian Maps in Hermitian Geometry, an

Автор: Sahin, Bayram
Название: Riemannian Submersions, Riemannian Maps in Hermitian Geometry, an
ISBN: 0128043911 ISBN-13(EAN): 9780128043912
Издательство: Elsevier Science
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Цена: 11706.00 р.
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Описание: Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications is a rich and self-contained exposition of recent developments in Riemannian submersions and maps relevant to complex geometry, focusing particularly on novel submersions, Hermitian manifolds, and K\{a}hlerian manifolds. Riemannian submersions have long been an effective tool to obtain new manifolds and compare certain manifolds within differential geometry. For complex cases, only holomorphic submersions function appropriately, as discussed at length in Falcitelli, Ianus and Pastore’s classic 2004 book. . In this new book, Bayram Sahin extends the scope of complex cases with wholly new submersion types, including Anti-invariant submersions, Semi-invariant submersions, slant submersions, and Pointwise slant submersions, also extending their use in Riemannian maps. . The work obtains new properties of the domain and target manifolds and investigates the harmonicity and geodesicity conditions for such maps. It also relates these maps with discoveries in pseudo-harmonic maps. Results included in this volume should stimulate future research on Riemannian submersions and Riemannian maps.


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