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Verlag: International Press of Boston, Incorporated, 2010
ISBN 10: 1571461817 ISBN 13: 9781571461810
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In den WarenkorbPaperback. Zustand: New. The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry. Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field.
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Sprache: Englisch
Verlag: Springer Berlin Heidelberg, 1991
ISBN 10: 3540550178 ISBN 13: 9783540550174
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Geometric Topology can be defined to be the investigation ofglobal properties of a further structure (e.g.differentiable, Riemannian, complex,algebraic etc.) one canimpose on a topological manifold. At the C.I.M.E. session inMontecatini, in 1990, three courses of lectures were givenonrecent developments in this subject which is nowadaysemerging as one of themost fascinating and promising fieldsof contemporary mathematics. The notesof these courses arecollected in this volume and can be described as: 1) thegeometry and the rigidity of discrete subgroups in Liegroups especially in the case of lattices in semi-simplegroups; 2) the study of the critical points of the distancefunction and its appication to the understanding of thetopology of Riemannian manifolds; 3) the theory of modulispace of instantons as a tool for studying the geometry oflow-dimensional manifolds.CONTENTS: J. Cheeger: Critical Points of Distance Functionsand Applications to Geometry.- M. Gromov, P. Pansu, Rigidityof Lattices: An Introduction.- Chr. Okonek: InstantonInvariants and Algebraic Surfaces.
Sprache: Englisch
Verlag: American Mathematical Society, 2025
ISBN 10: 1470481111 ISBN 13: 9781470481117
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ISBN 10: 1470481111 ISBN 13: 9781470481117
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Paperback. Zustand: new. Paperback. The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry. Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field. Explore the intricate interplay between curvature, topology, and global geometry in complete Riemannian manifolds. Early chapters introduce foundational aspects like Riemannian geometry, Toponogov's theorem, homogeneous spaces, and Morse theory, while later sections analyze rigidity phenomena and pivotal results from 19591974. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
Sprache: Englisch
Verlag: International Press of Boston, 2010
ISBN 10: 1571461817 ISBN 13: 9781571461810
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Taschenbuch. Zustand: Neu. Geometric Topology: Recent Developments | Lectures given on the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Monteca- tini Terme, Italy, June 4-12, 1990 | Jeff Cheeger (u. a.) | Taschenbuch | Lecture Notes in Mathematics | Einband - flex.(Paperback) | Englisch | 1991 | Springer | EAN 9783540550174 | Verantwortliche Person für die EU: Springer Nature Customer Service Center GmbH, Europaplatz 3, 69115 Heidelberg, productsafety[at]springernature[dot]com | Anbieter: preigu.
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In den WarenkorbPaperback. Zustand: new. Paperback. The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry. Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field. Explore the intricate interplay between curvature, topology, and global geometry in complete Riemannian manifolds. Early chapters introduce foundational aspects like Riemannian geometry, Toponogov's theorem, homogeneous spaces, and Morse theory, while later sections analyze rigidity phenomena and pivotal results from 19591974. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.
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In den WarenkorbPaperback. Zustand: New. The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry. Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field.
Sprache: Englisch
Verlag: American Elsevier Pub. Co, 1975
ISBN 10: 0444107649 ISBN 13: 9780444107640
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Zustand: Bon. Ancien livre de bibliothèque avec équipements. Couverture différente. Edition 1975. Tome 9. Ammareal reverse jusqu'à 15% du prix net de cet article à des organisations caritatives. ENGLISH DESCRIPTION Book Condition: Used, Good. Former library book. Different cover. Edition 1975. Volume 9. Ammareal gives back up to 15% of this item's net price to charity organizations.
Sprache: Englisch
Verlag: American Mathematical Society, Providence, 2025
ISBN 10: 1470481111 ISBN 13: 9781470481117
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Paperback. Zustand: new. Paperback. The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry. Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field. Explore the intricate interplay between curvature, topology, and global geometry in complete Riemannian manifolds. Early chapters introduce foundational aspects like Riemannian geometry, Toponogov's theorem, homogeneous spaces, and Morse theory, while later sections analyze rigidity phenomena and pivotal results from 19591974. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.
Verlag: International Press, Sommerville, MA, 2007
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In den WarenkorbHardcover. Zustand: Very Good. Hardcover (printed boards, no jacket) in very good condition. Surveys in Differential Geometry, Volume 11. A few light marks on the page block. The pages are clean and sound, all text is clear. CM. Used.
Sprache: Englisch
Verlag: Springer Berlin Heidelberg, 1991
ISBN 10: 3540550178 ISBN 13: 9783540550174
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In den WarenkorbZustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Critical points of distance functions and applications to geometry.- Rigidity of lattices: An introduction.- Instanton invariants and algebraic surfaces.Geometric Topology can be defined to be the investigation ofglobal properties of a further.
Sprache: Englisch
Verlag: Springer, Springer Spektrum Dez 1991, 1991
ISBN 10: 3540550178 ISBN 13: 9783540550174
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Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Geometric Topology can be defined to be the investigation of global properties of a further structure (e.g. differentiable, Riemannian, complex,algebraic etc.) one can impose on a topological manifold. At the C.I.M.E. session in Montecatini, in 1990, three courses of lectures were given onrecent developments in this subject which is nowadays emerging as one of themost fascinating and promising fields of contemporary mathematics. The notesof these courses are collected in this volume and can be described as: 1) the geometry and the rigidity of discrete subgroups in Lie groups especially in the case of lattices in semi-simple groups; 2) the study of the critical points of the distance function and its appication to the understanding of the topology of Riemannian manifolds; 3) the theory of moduli space of instantons as a tool for studying the geometry of low-dimensional manifolds. CONTENTS: J. Cheeger: Critical Points of Distance Functions and Applications to Geometry.- M. Gromov, P. Pansu, Rigidity of Lattices: An Introduction.- Chr. Okonek: Instanton Invariants and Algebraic Surfaces.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 208 pp. Englisch.