Riemannian Manifolds and Homogeneous Geodesics, Berestovskii Valerii, Nikonorov Yurii

Автор: Lee, John M.
Название: Introduction to riemannian manifolds
ISBN: 3319917544 ISBN-13(EAN): 9783319917542
Издательство: Springer
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Описание: It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet`s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Автор: Lee John M.
Название: Introduction to Riemannian Manifolds
ISBN: 3030801063 ISBN-13(EAN): 9783030801069
Издательство: Springer
Цена: 46570.00 T
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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: Philippe Tondeur
Название: Foliations on Riemannian Manifolds
ISBN: 0387967079 ISBN-13(EAN): 9780387967073
Издательство: Springer
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Цена: 97820.00 T
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Описание: Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena.

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
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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: Berestovskii Valerii, Nikonorov Yurii
Название: Riemannian Manifolds and Homogeneous Geodesics
ISBN: 3030566579 ISBN-13(EAN): 9783030566579
Издательство: Springer
Цена: 130430.00 T
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Описание: Introduction. - 1 Riemannian Manifolds. - 2 Lie Groups and Lie Algebras. - 3 Isometric Flows and Killing Vector Fields on Riemannian Manifolds. - 4 Homogeneous Riemannian Manifolds. - 5 Manifolds With Homogeneous Geodesics. - 6 Generalized Normal Homogeneous ManifoldsWith Intrinsic Metrics. - 7 Clifford-Wolf Homogeneous Riemannian Manifolds. - References. - List of Tables. - Index.

Автор: Giovanni Calvaruso; Marco Castrill?n L?pez
Название: Pseudo-Riemannian Homogeneous Structures
ISBN: 3030181510 ISBN-13(EAN): 9783030181512
Издательство: Springer
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Цена: 83850.00 T
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Описание: This book provides an up-to-date presentation of homogeneous pseudo-Riemannian structures, an essential tool in the study of pseudo-Riemannian homogeneous spaces. Benefiting from large symmetry groups, these spaces are of high interest in Geometry and Theoretical Physics.Since the seminal book by Tricerri and Vanhecke, the theory of homogeneous structures has been considerably developed and many applications have been found. The present work covers a gap in the literature of more than 35 years, presenting the latest contributions to the field in a modern geometric approach, with special focus on manifolds equipped with pseudo-Riemannian metrics.This unique reference on the topic will be of interest to researchers working in areas of mathematics where homogeneous spaces play an important role, such as Differential Geometry, Global Analysis, General Relativity, and Particle Physics.

Автор: Calvaruso Giovanni, Castrillуn Lуpez Marco
Название: Pseudo-Riemannian Homogeneous Structures
ISBN: 3030181545 ISBN-13(EAN): 9783030181543
Издательство: Springer
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Описание: This book provides an up-to-date presentation of homogeneous pseudo-Riemannian structures, an essential tool in the study of pseudo-Riemannian homogeneous spaces.

Автор: Ruzhansky Michael, Suragan Durvudkhan
Название: Hardy Inequalities on Homogeneous Groups: 100 Years of Hardy Inequalities
ISBN: 3030028941 ISBN-13(EAN): 9783030028947
Издательство: Springer
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Цена: 46570.00 T
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Описание: This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general H?rmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Автор: J?rg Winkelmann
Название: The Classification of Three-dimensional Homogeneous Complex Manifolds
ISBN: 3540590722 ISBN-13(EAN): 9783540590729
Издательство: Springer
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Цена: 41920.00 T
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Описание: This monograph provides classifications of all three-dimensional complex manifolds for which a transitive action of a Lie group exists. The classifications are based on methods from Lie group theory, complex analysis and algebraic geometry.

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
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Цена: 142560.00 T
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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: Chen Bang-yen
Название: Differential Geometry Of Warped Product Manifolds And Submanifolds
ISBN: 9813208929 ISBN-13(EAN): 9789813208926
Издательство: World Scientific Publishing
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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: John Douglas Moore
Название: Introduction to Global Analysis: Minimal Surfaces in Riemannian Manifolds
ISBN: 1470429500 ISBN-13(EAN): 9781470429508
Издательство: Mare Nostrum (Eurospan)
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Цена: 112860.00 T
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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.