1 edition of **Global Riemannian Geometry: Curvature and Topology** found in the catalog.

- 308 Want to read
- 8 Currently reading

Published
**2003**
by Birkhäuser Basel in Basel
.

Written in English

- Global differential geometry,
- Mathematics,
- Cell aggregation,
- Global analysis

**Edition Notes**

Statement | edited by Steen Markvorsen, Maung Min-Oo |

Series | Advanced Courses in Mathematics - CRM Barcelona, Advanced courses in mathematics, CRM Barcelona |

Contributions | Min-Oo, Maung |

Classifications | |
---|---|

LC Classifications | QA614-614.97 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (100 pages). |

Number of Pages | 100 |

ID Numbers | |

Open Library | OL27041494M |

ISBN 10 | 3034880553 |

ISBN 10 | 9783034880558 |

OCLC/WorldCa | 840290347 |

Get this from a library! Global Riemannian Geometry: Curvature and Topology. [Steen Markvorsen; Maung Min-Oo] -- The book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in. It also shows very nicely how curvature bounds can be used with Sturm-Liouville theory applied to Jacobi fields along a geodesic to establish global geometric properties of a Riemannian manifold. This is the heart of global Riemannian geometry as developed by Berger, Toponogov, and others and raised to a high art by Gromov and Perelman among.

Lectures on Geodesics Riemannian Geometry. Aim of this book is to give a fairly complete treatment of the foundations of Riemannian geometry through the tangent bundle and the geodesic flow on it. Topics covered includes: Sprays, Linear connections, Riemannian manifolds, Geodesics, Canonical connection, Sectional Curvature and metric structure. Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a .

This text is designed for a one-quarter or one-semester graduate course on Riemannian geometry. It focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced study of Riemannian s: 5. The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. Customer reviews. out of 5 stars. 3 out of 5. 5 customer ratings. 5 star 32% (32%) 32% 4 star 0% (0% Reviews: 5.

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Global Riemannian Geometry: Curvature and Topology Authors: Hurtado, A., Markvorsen, S., Min-Oo, M., Palmer, V. Discussion of the Laplacian as a 'swift' operator on minimal submanifolds in ambient spaces with small sectional curvatures.

Global Riemannian Geometry: Curvature and Topology (Advanced Courses in Mathematics - CRM Barcelona) rd Edition by Steen Markvorsen (Author) › Visit Amazon's Steen Markvorsen Page.

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Global Riemannian Geometry: Curvature and Topology. Authors (view affiliations) Steen Markvorsen; Maung Min-Oo Search within book. Front Matter. Pages i-viii. PDF. Distance Geometric Analysis on Manifolds Maung Min-Oo. Pages Back Matter. Pages PDF.

About this book. Keywords. Differential Topology Global Analysis Riemannian. Global Riemannian Geometry: Curvature and Topology. Authors: Markvorsen, Steen, Min-Oo, Maung Free PreviewBrand: Birkhäuser Basel. [PDF] Global Riemannian Geometry: Curvature and Topology Global Riemannian Geometry: Curvature and Topology Book Review Without doubt, this is actually the greatest function by any article writer.

It is among the most amazing publication i have got read. Its been printed in an exceedingly basic way in fact it is simply after i finished. 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.

For a Riemannian manifold \(M\), the geometry, topology and analysis are interrelated in ways that are widely explored in modern mathematics. Bounds on the curvature can have significant implications for the topology of the manifold.

The eigenvalues of the Laplacian are naturally linked to the geometry of the manifold. The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications.

Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist.

The works in this series are addressed to advanced students and researchers. The book is probably one of the most easily accessible introductions to Riemannian geometry.

(M.C. Leung, MathReview) The book’s aim is to develop tools and intuition for studying the central unifying theme in Riemannian geometry, which is the notion of curvature and its relation with topology. Lectures on Differential Geometry by John Douglas Moore - University of California Foundations of Riemannian geometry, including geodesics and curvature, as well as connections in vector bundles, and then go on to discuss the relationships between curvature and topology.

Topology will presented in two dual contrasting forms. ( views). Description. Differential topology considers the properties and structures that require only a smooth structure on a manifold to be defined.

Smooth manifolds are 'softer' than manifolds with extra geometric structures, which can act as obstructions to certain types of equivalences and deformations that exist in differential topology.

For instance, volume and Riemannian curvature. 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.

Comparison Theorems in Riemannian Geometry About this Title. Jeff Cheeger, New York University - Courant Institute, New York, NY and David G.

Ebin, State University of New York at Stony Brook, Stony Brook, NY. Publication: AMS Chelsea Publishing Publication Year:. 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 Reviews: 7.

Our general research interests lie in the realms of global differential geometry, Riemannian geometry, geometric topology, and their applications. Current topics under investigation include, e.g., questions concerning the geometry and topology of nonnegative and almost nonnegative curvature, singular metric spaces, collapsing and Gromov.

ISBN: OCLC Number: Description: 87 pages: illustrations ; 24 cm. Contents: Distance Geometric Analysis on Manifolds / Steen Markvorsen Appetizer and Introduction The Comparison Setting and Preliminaries Analysis of Restricted Distance Functions Concerning the Setting and Notation This book is designed as a textbook for a one-quarter or one-semester graduate course on Riemannian geometry, for students who are familiar with topological and differentiable manifolds.

It focuses on developing an intimate acquaintance with the geometric meaning of curvature. Foundations of Riemannian geometry, including geodesics and curvature, as well as connections in vector bundles, and then go on to discuss the relationships between curvature and topology.

Topology will presented in two dual contrasting forms. ( views) A Panoramic View of Riemannian Geometry by Marcel Berger - Springer, The core part, Differential Geometry, covers Riemannian Geometry, Global Analysis and Geometric Analysis.

A central topic in Riemannian geometry is the interplay between curvature and topology of Riemannian manifolds and spaces. A well-known example is the classical Bonnet-Myers theorem which states that a complete Riemannian manifold of.

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/5(4).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."This book is based on a graduate course on Riemannian geometry and analysis on manifolds that was held in Paris.

Classical results on the relations between curvature and topology are treated in detail. The book is almost self-contained, assuming in general only basic calculus. It contains nontrivial exercises with full solutions at the s: 8.