Introduction to riemannian manifolds, Lee, John M.
Автор: Lee John M. Название: Introduction to Riemannian Manifolds ISBN: 3030801063 ISBN-13(EAN): 9783030801069 Издательство: Springer Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Thisbookisdesignedasatextbookforaone-quarterorone-semestergr- uate course on Riemannian geometry, for students who are familiar with topological and di?erentiable manifolds. It focuses on developing an in- mate acquaintance with the geometric meaning of curvature. In so doing, it introduces and demonstrates the uses of all the main technical tools needed for a careful study of Riemannian manifolds. I have selected a set of topics that can reasonably be covered in ten to ?fteen weeks, instead of making any attempt to provide an encyclopedic treatment of the subject. The book begins with a careful treatment of the machineryofmetrics, connections, andgeodesics, withoutwhichonecannot claim to be doing Riemannian geometry. It then introduces the Riemann curvature tensor, and quickly moves on to submanifold theory in order to give the curvature tensor a concrete quantitative interpretation. From then on, all e?orts are bent toward proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet theorem (expressing thetotalcurvatureofasurfaceintermsofitstopologicaltype), theCartan- Hadamard theorem (restricting the topology of manifolds of nonpositive curvature), Bonnet's theorem (giving analogous restrictions on manifolds of strictly positive curvature), and a special case of the Cartan-Ambrose- Hicks theorem (characterizing manifolds of constant curvature). Many other results and techniques might reasonably claim a place in an introductory Riemannian geometry course, but could not be included due to time constraints.
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.
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: Andrei Agrachev, Davide Barilari, Ugo Boscain Название: A Comprehensive Introduction to Sub-Riemannian Geometry ISBN: 110847635X ISBN-13(EAN): 9781108476355 Издательство: Cambridge Academ Рейтинг: Цена: 185850.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This comprehensive introduction to sub-Riemannian geometry proceeds from classical topics to cutting-edge theory and applications. The only prerequisites are calculus, linear algebra and differential equations. It can be used for graduate courses in Riemannian or sub-Riemannian geometry, or as a reference for researchers in several disciplines.
This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings:
ODE theory;
Maximum Principles (weak, strong and propagation principles);
Lie groups (with an emphasis on the construction of Lie groups).
This book also provides an introduction to the basic theory of Geometrical Analysis, with a new foundational presentation based on Ordinary Differential Equation techniques, in a unitary and self-contained way.
The book also contains:
58 figures;
182 exercises;
3 Appendices;
a Further Reading section.
Автор: Shen Yi-Bing Et Al Название: Introduction To Modern Finsler Geometry ISBN: 9814704903 ISBN-13(EAN): 9789814704908 Издательство: World Scientific Publishing Рейтинг: Цена: 69690.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.
In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.
Автор: Shen Yi-Bing Et Al Название: Introduction To Modern Finsler Geometry ISBN: 9814713163 ISBN-13(EAN): 9789814713160 Издательство: World Scientific Publishing Цена: 42240.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.
In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.
Автор: Serge Lang Название: Differential and Riemannian Manifolds ISBN: 1461286883 ISBN-13(EAN): 9781461286882 Издательство: Springer Рейтинг: Цена: 55850.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book covers basic concepts in differential topology, differential geometry and differential equations. The latest, expanded edition offers three new chapters on Riemannian and pseudo-Riemannian geometry, and revised sections on sprays and Stokes` theorem.
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: Krzysztof Galicki; Santiago R. Simanca Название: Riemannian Topology and Geometric Structures on Manifolds ISBN: 0817647422 ISBN-13(EAN): 9780817647421 Издательство: Springer Рейтинг: Цена: 139750.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kahler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory.
Автор: Javier de Lucas, Cristina Sardon Munoz Название: A Guide to Lie Systems with Compatible Geometric Structures ISBN: 1786346974 ISBN-13(EAN): 9781786346971 Издательство: World Scientific Publishing Рейтинг: Цена: 142560.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics. It embraces several basic topics on differential geometry and the study of geometric structures while developing known applications in the theory of Lie systems. The book also includes a brief exploration of the applications of Lie systems to superequations, discrete systems, and partial differential equations.
Offering a complete overview from the topic's foundations to the present, this book is an ideal resource for Physics and Mathematics students, doctoral students and researchers.
Автор: Chris Wendl Название: Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory ISBN: 1108497403 ISBN-13(EAN): 9781108497404 Издательство: Cambridge Academ Рейтинг: Цена: 121440.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Based on a series of lectures for students in topology, this book provides an entry point into the intersection theory of punctured holomorphic curves. Appendices featuring quick reference guides for applying the theory and self-contained proofs of key technical results also make it a valuable resource for researchers.
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