A Comprehensive Introduction to Sub-Riemannian Geometry, Andrei Agrachev, Davide Barilari, Ugo Boscain

Автор: Andre Bellaiche; Jean-Jaques Risler
Название: Sub-Riemannian Geometry
ISBN: 3034899467 ISBN-13(EAN): 9783034899468
Издательство: Springer
Рейтинг:
Цена: 130430.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
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

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
Рейтинг:
Цена: 46570.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
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.

Автор: Chen Bang-yen
Название: Differential Geometry Of Warped Product Manifolds And Submanifolds
ISBN: 9813208929 ISBN-13(EAN): 9789813208926
Издательство: World Scientific Publishing
Рейтинг:
Цена: 174240.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:

A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry -- except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson-Walker models, are warped product manifolds.

The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson-Walker's and Schwarzschild's.

The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century.

The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.

Автор: J?rgen Jost
Название: Riemannian Geometry and Geometric Analysis
ISBN: 3319618598 ISBN-13(EAN): 9783319618593
Издательство: Springer
Рейтинг:
Цена: 79190.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This established reference work continues to introduce its readers to some of the hottest topics in contemporary mathematical research. This sixth edition includes, among other new additions, a systematic treatment of eigenvalues of Riemannian manifolds.

Автор: John Douglas Moore
Название: Introduction to Global Analysis: Minimal Surfaces in Riemannian Manifolds
ISBN: 1470429500 ISBN-13(EAN): 9781470429508
Издательство: Mare Nostrum (Eurospan)
Рейтинг:
Цена: 112860.00 T
Наличие на складе: Невозможна поставка.
Описание: During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold $M$ determine the homology of the manifold.Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on $M$ by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs.This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed parametrized minimal surfaces in a compact Riemannian manifold, establishing Morse inequalities for perturbed versions of the energy function on the mapping space. It studies the bubbling which occurs when the perturbation is turned off, together with applications to the existence of closed minimal surfaces. The Morse-Sard theorem is used to develop transversality theory for both closed geodesics and closed minimal surfaces.This book is based on lecture notes for graduate courses on "Topics in Differential Geometry", taught by the author over several years. The reader is assumed to have taken basic graduate courses in differential geometry and algebraic topology.

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
Рейтинг:
Цена: 93160.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
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.

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
Рейтинг:
Цена: 102480.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
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.

Автор: Lyndon Woodward, John Bolton
Название: A First Course in Differential Geometry: Surfaces in Euclidean Space
ISBN: 1108424937 ISBN-13(EAN): 9781108424936
Издательство: Cambridge Academ
Рейтинг:
Цена: 80250.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This textbook covers the classical topics of differential geometry of surfaces as studied by Gauss: the definition and geometric meaning of Gaussian curvature, the Theorema Egregium, geodesics, and the Gauss-Bonnet Theorem. It is suitable for upper-level undergraduates and contains plentiful examples and exercises, with solutions to selected problems.

Автор: Pietro Giuseppe Fre, Alexander Fedotov
Название: Groups and Manifolds: Lectures for Physicists with Examples in Mathematica
ISBN: 3110551195 ISBN-13(EAN): 9783110551198
Издательство: Walter de Gruyter
Цена: 99110.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Groups and Manifolds is an introductory, yet a complete self-contained course on mathematics of symmetry: group theory and differential geometry of symmetric spaces, with a variety of examples for physicists, touching briefly also on super-symmetric field theories. The core of the course is focused on the construction of simple Lie algebras, emphasizing the double interpretation of the ADE classification as applied to finite rotation groups and to simply laced simple Lie algebras. Unique features of this book are the full-fledged treatment of the exceptional Lie algebras and a rich collection of MATHEMATICA Notebooks implementing various group theoretical constructions.

Автор: Sahin, Bayram
Название: Riemannian Submersions, Riemannian Maps in Hermitian Geometry, an
ISBN: 0128043911 ISBN-13(EAN): 9780128043912
Издательство: Elsevier Science
Рейтинг:
Цена: 78040.00 T
Наличие на складе: Поставка под заказ.
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.

Автор: Thierry Aubin
Название: Some Nonlinear Problems in Riemannian Geometry
ISBN: 364208236X ISBN-13(EAN): 9783642082368
Издательство: Springer
Рейтинг:
Цена: 121070.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: During the last few years, the field of nonlinear problems has undergone great development. This book consisting of the updated Grundlehren volume 252 by the author and of a newly written part, deals with some important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved. Each problem is explained, up-to-date results are given and proofs are presented. Thus, the reader is given access, for each specific problem, to its present status of solution as well as to the most up-to-date methods for approaching it. The main objective of the book is to explain some methods and new techniques, and to apply them. It deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber.

Автор: Godinho Leonor
Название: Introduction to Riemannian Geometry
ISBN: 3319086650 ISBN-13(EAN): 9783319086651
Издательство: Springer
Рейтинг:
Цена: 65210.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity.The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature.