Moduli Spaces Of Riemannian Metrics
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Moduli Spaces Of Riemannian Metrics
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Author : Wilderich Tuschmann
language : en
Publisher: Springer
Release Date : 2015-10-14
Moduli Spaces Of Riemannian Metrics written by Wilderich Tuschmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-14 with Mathematics categories.
This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research.
Riemannian Metrics Of Constant Mass And Moduli Spaces Of Conformal Structures
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Author : Lutz Habermann
language : en
Publisher: Springer
Release Date : 2007-05-06
Riemannian Metrics Of Constant Mass And Moduli Spaces Of Conformal Structures written by Lutz Habermann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
This monograph deals with recent questions of conformal geometry. It provides in detail an approach to studying moduli spaces of conformal structures, using a new canonical metric for conformal structures. This book is accessible to readers with basic knowledge in differential geometry and global analysis. It addresses graduates and researchers.
Geometry And Physics
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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-17
Geometry And Physics written by Jürgen Jost 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 2009-08-17 with Mathematics categories.
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
On The Global Topology Of Moduli Spaces Of Riemannian Metrics With Holonomy Sp N
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Author : David Degen
language : en
Publisher:
Release Date : 2022*
On The Global Topology Of Moduli Spaces Of Riemannian Metrics With Holonomy Sp N written by David Degen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022* with categories.
On Spaces And Moduli Spaces Of Riemannian Metrics Satisfying Curvature Conditions
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Author : Jan-Bernhard Kordaß
language : en
Publisher:
Release Date : 2018
On Spaces And Moduli Spaces Of Riemannian Metrics Satisfying Curvature Conditions written by Jan-Bernhard Kordaß and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Metric Structures For Riemannian And Non Riemannian Spaces
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Author : Mikhail Gromov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-25
Metric Structures For Riemannian And Non Riemannian Spaces written by Mikhail Gromov 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 2007-06-25 with Mathematics categories.
Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory. The new wave began with seminal papers by Svarc and Milnor on the growth of groups and the spectacular proof of the rigidity of lattices by Mostow. This progress was followed by the creation of the asymptotic metric theory of infinite groups by Gromov. The structural metric approach to the Riemannian category, tracing back to Cheeger's thesis, pivots around the notion of the Gromov–Hausdorff distance between Riemannian manifolds. This distance organizes Riemannian manifolds of all possible topological types into a single connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov and Perelman. Also, Gromov found metric structure within homotopy theory and thus introduced new invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degrees of maps between manifolds. During the same period, Banach spaces and probability theory underwent a geometric metamorphosis, stimulated by the Levy–Milman concentration phenomenon, encompassing the law of large numbers for metric spaces with measures and dimensions going to infinity. The first stages of the new developments were presented in Gromov's course in Paris, which turned into the famous "Green Book" by Lafontaine and Pansu (1979). The present English translation of that work has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices – by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures – as well as an extensive bibliographyand index round out this unique and beautiful book.
On The Global Topology Of Moduli Spaces Of Riemannian Metrics With Holonomy Operatorname Sp N
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Author : David Degen
language : en
Publisher:
Release Date : 2023
On The Global Topology Of Moduli Spaces Of Riemannian Metrics With Holonomy Operatorname Sp N written by David Degen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
Metric Foliations And Curvature
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Author : Detlef Gromoll
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-28
Metric Foliations And Curvature written by Detlef Gromoll 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 2009-03-28 with Mathematics categories.
Riemannian manifolds, particularly those with positive or nonnegative curvature, are constructed from only a handful by means of metric fibrations or deformations thereof. This text documents some of these constructions, many of which have only appeared in journal form. The emphasis is less on the fibration itself and more on how to use it to either construct or understand a metric with curvature of fixed sign on a given space.
Einstein Manifolds
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Author : Arthur L. Besse
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-03
Einstein Manifolds written by Arthur L. Besse 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 2007-12-03 with Mathematics categories.
Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. This is the first book which presents an overview of several striking results ensuing from the examination of Einstein’s equations in the context of Riemannian manifolds. Parts of the text can be used as an introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals.
The Geometry Of Moduli Spaces Of Sheaves
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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-27
The Geometry Of Moduli Spaces Of Sheaves written by Daniel Huybrechts 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 2010-05-27 with Mathematics categories.
This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.