Автор: Lang Serge Название: Fundamentals of Differential Geometry ISBN: 038798593X ISBN-13(EAN): 9780387985930 Издательство: Springer Рейтинг: Цена: 8881 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Providing an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas, Langs presentation, unique writing style, and elegant proofs enables readers to obtain a thorough understanding of the topic. This new edition of this classic work includes new chapters, sections, examples, and exercises.
Описание: In this book the authors study the differential geometry of varieties with degenerate Gauss maps. They use the main methods of differential geometry, namely, the methods of moving frames and exterior differential forms as well as tensor methods. By means of these methods, the authors discover the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.The authors introduce the above mentioned methods and apply them to a series of concrete problems arising in the theory of varieties with degenerate Gauss maps. What makes this book unique is the authorsвЂ™ use of a systematic application of methods of projective differential geometry along with methods of the classical algebraic geometry for studying varieties with degenerate Gauss maps.This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.
Автор: Walschap Gerard Название: Metric Structures in Differential Geometry ISBN: 038720430X ISBN-13(EAN): 9780387204307 Издательство: Springer Рейтинг: Цена: 8359 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This text is an introduction to the theory of differentiable manifolds and fiber bundles. The only requisites are a solid background in calculus and linear algebra, together with some basic point-set topology. The first chapter provides a comprehensive overview of differentiable manifolds. The following two chapters are devoted to fiber bundles and homotopy theory of fibrations. Vector bundles have been emphasized, although principal bundles are also discussed in detail. The last three chapters study bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres. Chapter 5, with its focus on the tangent bundle, also serves as a basic introduction to Riemannian geometry in the large. This book can be used for a one-semester course on manifolds or bundles, or a two-semester course in differential geometry.Gerard Walschap is Professor of Mathematics at the University of Oklahoma where he developed this book for a series of graduate courses he has taught over the past few years.
Описание: This book is a comprehensive report of recent developments in Finsler geometry and Spray geometry. Riemannian geometry and pseudo-Riemannian geometry are treated as the special case of Finsler geometry. The geometric methods developed in this subject are useful for studying some problems arising from biology, physics, and other fields. Audience: The book will be of interest to graduate students and mathematicians in geometry who wish to go beyond the Riemannian world. Scientists in nature sciences will find the geometric methods presented useful.
Автор: Svec A. Название: Global Differential Geometry of Surfaces ISBN: 1402003188 ISBN-13(EAN): 9781402003189 Издательство: Springer Рейтинг: Цена: 5224 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: It may be said that almost all results are new and belong to myself (the exceptions being the introductory three chapters, the few classical results and results of my post- graduate student Mr. M.
Описание: This book is based on a series of lectures delivered over the years by the author at the University Pierre et Marie Curie in Paris, at the University of Stuttgart, and at City University of Hong Kong. Its two-fold aim is to provide a thorough introduction to the basic theorems of differential geometry and to elasticity in curvilinear coordinates and shell theory. To this end, the fundamental existence and uniqueness theorems are proved in great details. Such theorems include the fundamental theorem of surface theory, which asserts that the Gauss and Codazzi-Mainardi equations are sufficient for the existence of a surface with prescribed fundamental forms, as well as the corresponding rigidity theorem. Recent results, which have not yet appeared in book form are also included, such as the continuity of a surface as a function of its fundamental forms.This book also provides a detailed description of the equations of nonlinear and linearized elasticity in curvilinear coordinates, together with a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The book also includes a detailed description of Koiter's equations for nonlinearly and linearly elastic shells, a complete analysis of the existence, uniqueness, and regularity of the solutions of Koiter's equations in the linear case.The treatment is essentially self-contained and proofs are complete. In particular, no a priori knowledge of diferential geometry or elasticity theory or shell theory is assumed. Another highlight of this book is the focus on the interplay between "theoretical" and "applied" differential geometry. For instance, rather than being introduced in a formal way, covariant derivatives of a tensor field appear in a natural way in the course of the derivation of the basic boundary value problems of nonlinear elasticity in curvilinear coordinates and of shell theory.
Автор: Anders Kock Название: Synthetic Differential Geometry ISBN: 0521687381 ISBN-13(EAN): 9780521687386 Издательство: Cambridge Academ Рейтинг: Цена: 5981 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Synthetic Differential Geometry is a method of reasoning in differential geometry and differential calculus, based on the assumption of sufficiently many nilpotent elements on the number line, in particular numbers d such that d2=0. The use of nilpotent elements allows one to replace the limit processes of calculus by purely algebraic calculations and notions. For the first half of the book familiarity with differential calculus and abstract algebra is presupposed during the development of results in calculus and differential geometry on a purely axiomatic/synthetic basis. In the second half basic notions of category theory are presumed in the construction of suitable Cartesian closed categories and the interpretation of logical formulae within them. This is a second edition of Kock's classical text from 1981. Many notes have been included, with comments on developments in the field from the intermediate years, and almost 100 new bibliographic entries have been added.
Автор: Udo Hertrich-Jeromin Название: Introduction to M?bius Differential Geometry ISBN: 0521535697 ISBN-13(EAN): 9780521535694 Издательство: Cambridge Academ Рейтинг: Цена: 7476 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for Mobius geometry are presented: the classical projective model, the quaternionic approach, and an approach that uses the Clifford algebra of the space of homogeneous coordinates of the classical model; the use of 2-by-2 matrices in this context is elaborated. For each model in turn applications are discussed. Topics comprise conformally flat hypersurfaces, isothermic surfaces and their transformation theory, Willmore surfaces, orthogonal systems and the Ribaucour transformation, as well as analogous discrete theories for isothermic surfaces and orthogonal systems. Certain relations with curved flats, a particular type of integrable system, are revealed. Thus this book will serve both as an introduction to newcomers (with background in Riemannian geometry and elementary differential geometry) and as a reference work for researchers.
Описание: Differential geometry has a long, wonderful history and has found relevance in many areas. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the standard university curriculum to a type of mathematics that is a unified whole, by mixing geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors, but also for students in engineering and the sciences. Into the mix of these ideas comes the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.
Автор: V. Ovsienko Название: Projective Differential Geometry Old and New ISBN: 0521831865 ISBN-13(EAN): 9780521831864 Издательство: Cambridge Academ Рейтинг: Цена: 11273 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal is to emphasize connections between
classical projective differential geometry and contemporary mathematics and mathematical physics. They also give new results and new proofs of classic theorems.
play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the
Virasoro algebra. One-dimensional projective differential geometry features strongly.
Related topics include differential operators, the cohomology of the group of
diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures.
A final chapter considers various versions of multi-dimensional Schwarzian derivative.
In sum, here is a ra
id route for graduate students and researchers to the frontiers of current research in this evergreen subject.
Описание: Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology).
Описание: In view of the significance of the array manifold in array processing and array communications, the role of differential geometry as an analytical tool cannot be
overemphasized. Differential geometry is mainly confined to the investigation of the geometric properties of manifolds in three-dimensional Euclidean space R3 and in real spaces of
higher dimension. Extending the theoretical framework to complex spaces, this invaluable book presents a summary of those results of differential geometry which are of practical interest
in the study of linear, planar and three-dimensional array geometries.
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