riemannian geometry a modern introduction cambridge studies in advanced mathematics

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Riemannian Geometry

Author : Isaac Chavel
ISBN : 9781139452571
Genre : Mathematics
File Size : 53. 54 MB
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This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.

Introduction To Smooth Manifolds

Author : John Lee
ISBN : 9781441999825
Genre : Mathematics
File Size : 33. 79 MB
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This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard’s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.

Function Spaces And Partial Differential Equations

Author : Ali Taheri
ISBN : 9780198733157
Genre : Differential equations, Partial
File Size : 27. 19 MB
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This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Needle Decompositions In Riemannian Geometry

Author : Bo’az Klartag
ISBN : 9781470425425
Genre : Curvature
File Size : 59. 47 MB
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The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.

Elementare Differentialgeometrie

Author : Christian Bär
ISBN : 9783110224597
Genre : Mathematics
File Size : 36. 38 MB
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This textbook presents an introduction to the differential geometry of curves and surfaces. This second, revised edition has been expanded to include solutions and applications in cartography. Topics include Euclidean geometry, curve theory, surface theory, curvature concepts, minimal surfaces, Riemann geometry and the Gauss-Bonnet theorem.

Differential Geometry And Lie Groups For Physicists

Author : Marián Fecko
ISBN : 9781139458030
Genre : Science
File Size : 46. 85 MB
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Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses.

Differentialgeometrie Von Kurven Und Fl Chen

Author : Manfredo P. do Carmo
ISBN : 9783322850720
Genre : Technology & Engineering
File Size : 46. 42 MB
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Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang

A Course In Modern Mathematical Physics

Author : Peter Szekeres
ISBN : 0521829607
Genre : Mathematics
File Size : 88. 51 MB
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This book provides an introduction to the mathematics of modern physics, presenting concepts and techniques in mathematical physics at a level suitable for advanced undergraduates and beginning graduate students. It aims to introduce the reader to modern mathematical thinking within a physics setting. Topics covered include tensor algebra, differential geometry, topology, Lie groups and Lie algebras, distribution theory, fundamental analysis and Hilbert spaces. The book includes exercises and worked examples, to test the students' understanding of the various concepts, as well as extending the themes covered in the main text.

Geometry Analysis And Topology Of Discrete Groups

Author : Lizhen Ji
ISBN : 1571461264
Genre : Mathematics
File Size : 64. 75 MB
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Discrete subgroups of Lie groups are foundational objects in modern mathematics and occur naturally in different subjects. This new volume presents 15 papers treating discrete groups as they occur in areas such as algebra, analysis, geometry, number theory, and topology. Most of the papers are surveys, and the volume is intended to help graduate students and researchers better understand the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces.

Geometric Analysis

Author : Peter Li
ISBN : 9781107020641
Genre : Mathematics
File Size : 71. 62 MB
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Basic techniques for researchers interested in the field of geometric analysis.

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