Perspectives In Riemannian Geometry
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Perspectives In Riemannian Geometry
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Author : Vestislav Apostolov
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Perspectives In Riemannian Geometry written by Vestislav Apostolov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Special geometries as well as the relation between curvature and topology have always been of interest to differential geometers. More recently, these topics have turned out to be of use in physical problems related to string theory as well. This volume provides a unique and thorough survey on the latest developments on Riemannian geometry, special geometrical structures on manifolds, and their interactions with other fields such as mathematical physics, complex analysis, andalgebraic geometry. This volume presents ten papers written by participants of the ``Short Program on Riemannian Geometry,'' a workshop held at the CRM in Montreal in 2004. It will be a valuable reference for graduate students and research mathematicians alike. Information for our distributors: Titles inthis series are copublished with the Centre de Recherches Mathematiques.
Differential Geometry And Lie Groups
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Author : Jean Gallier
language : en
Publisher: Springer Nature
Release Date : 2020-08-18
Differential Geometry And Lie Groups written by Jean Gallier and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-18 with Mathematics categories.
This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.
Manifolds Sheaves And Cohomology
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Author : Torsten Wedhorn
language : en
Publisher: Springer
Release Date : 2016-07-25
Manifolds Sheaves And Cohomology written by Torsten Wedhorn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Mathematics categories.
This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.
Riemannian Geometry
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Author : Isaac Chavel
language : en
Publisher: Cambridge University Press
Release Date : 1995-01-27
Riemannian Geometry written by Isaac Chavel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-27 with Mathematics categories.
This book provides an introduction to Riemannian geometry, the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and those new notions and ideas motivated by curvature itself. Isoperimetric inequalities--the interplay of curvature with volume of sets and the areas of their boundaries--is reviewed along with other specialized classical topics. A number of completely new themes are created by curvature: they include local versus global geometric properties, that is, the interaction of microscopic behavior of the geometry with the macroscopic structure of the space. Also featured is an ambitious "Notes and Exercises" section for each chapter that will develop and enrich the reader's appetite and appreciation for the subject.
From Riemann To Differential Geometry And Relativity
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Author : Lizhen Ji
language : en
Publisher: Springer
Release Date : 2017-10-03
From Riemann To Differential Geometry And Relativity written by Lizhen Ji and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-03 with Mathematics categories.
This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
Isoperimetric Inequalities
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Author : Isaac Chavel
language : en
Publisher: Cambridge University Press
Release Date : 2001-07-23
Isoperimetric Inequalities written by Isaac Chavel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-23 with Mathematics categories.
This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.
A Perspective On Canonical Riemannian Metrics
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Author : Giovanni Catino
language : en
Publisher: Springer Nature
Release Date : 2020-10-23
A Perspective On Canonical Riemannian Metrics written by Giovanni Catino and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-23 with Mathematics categories.
This book focuses on a selection of special topics, with emphasis on past and present research of the authors on “canonical” Riemannian metrics on smooth manifolds. On the backdrop of the fundamental contributions given by many experts in the field, the volume offers a self-contained view of the wide class of “Curvature Conditions” and “Critical Metrics” of suitable Riemannian functionals. The authors describe the classical examples and the relevant generalizations. This monograph is the winner of the 2020 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.
On The Hypotheses Which Lie At The Bases Of Geometry
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Author : Bernhard Riemann
language : en
Publisher: Birkhäuser
Release Date : 2016-04-19
On The Hypotheses Which Lie At The Bases Of Geometry written by Bernhard Riemann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.
From Differential Geometry To Non Commutative Geometry And Topology
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Author : Neculai S. Teleman
language : en
Publisher: Springer Nature
Release Date : 2019-11-10
From Differential Geometry To Non Commutative Geometry And Topology written by Neculai S. Teleman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-10 with Mathematics categories.
This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.
Differential And Riemannian Manifolds
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-03-09
Differential And Riemannian Manifolds written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-09 with Mathematics categories.
This is the third version of a book on Differential Manifolds; in this latest expansion three chapters have been added on Riemannian and pseudo-Riemannian geometry, and the section on sprays and Stokes' theorem have been rewritten. This text provides an introduction to basic concepts in differential topology, differential geometry and differential equations. In differential topology one studies classes of maps and the possibility of finding differentiable maps in them, and one uses differentiable structures on manifolds to determine their topological structure. In differential geometry one adds structures to the manifold (vector fields, sprays, a metric, and so forth) and studies their properties. In differential equations one studies vector fields and their integral curves, singular points, stable and unstable manifolds, and the like.