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Wednesday, August 5, 2020 | History

8 edition of Metric Structures in Differential Geometry found in the catalog.

Metric Structures in Differential Geometry

by Gerard Walschap

  • 398 Want to read
  • 3 Currently reading

Published by Springer .
Written in English


The Physical Object
Number of Pages232
ID Numbers
Open LibraryOL7444327M
ISBN 10038720430X
ISBN 109780387204307

They give a particularly useful presentation of metric-free differential geometry. The Misner/Thorne/Wheeler book presents the physicist's view of differential geometry (in addition to general relativity and cosmology). This book is noteworthy for apparently using no function spaces at all. They don't even use sets. A metric space M is called bounded if there exists some number r, such that d(x,y) ≤ r for all x and y in smallest possible such r is called the diameter of space M is called precompact or totally bounded if for every r > 0 there exist finitely many open balls of radius r whose union covers the set of the centres of these balls is finite, it has finite diameter, from.

Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Geometry and Differential Geometry | Conference on Geometry and Differential Geometry ( University of Haifa), Izu Vaisman, Rafael Artzy | download | .

Preface; 1. Exterior algebra; 2. Differential forms on open subsets of Rn; 3. Metric structures; 4. Gauge theories; 5. Einstein-Cartan theory; 6. The Lie derivative Cited by: differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a 5/5(1).


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Metric Structures in Differential Geometry by Gerard Walschap Download PDF EPUB FB2

There are so many books on graduate differential geometry,but most of the best ones are just too lengthy to be practical for use in a real graduate differential geometry course.

's 5 volume epic,John 's wonderful trilogy, Jeffery Lee's more recent text and Lawrence Conlon's excellent tome are all terrific choices for graduate by: Metric Structures in Differential Geometry.

Authors: Walschap, Gerard The last three chapters study bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle Brand: Springer-Verlag New York.

The last three chapters study bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory Metric Structures in Differential Geometry book discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle.

These concepts are illustrated in detail for bundles over spheres. Book Title:Metric Structures in Differential Geometry This text is an introduction to the theory of differentiable manifolds and fiber bundles. The only requisites are a solid background in calculus and linear algebra, together with some basic pointset topology.

Get this from a library. Metric structures in differential geometry. [Gerard Walschap] -- "This text is an introduction to the theory of differentiable manifolds and fiber bundles. The only requisites are a solid background in calculus and linear algebra, together with some basic. This book offers an introduction to the theory of differentiable manifolds and fiber bundles.

It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian Read more. Metric Structures in Differential Geometry 1st edition by Walschap, Gerard published by Springer Hardcover Hardcover – Ma out of 5 stars 2 ratings.

See all 7 formats and editions Hide other formats and editions. Price New from Used from eTextbook "Please retry" /5(2). Metric Structures in Differential Geometry (Graduate Texts in Mathematics Book ) Softcover reprint of the original 1st ed. Edition, Kindle Edition by Gerard Walschap (Author) Format: Kindle Edition.

out of 5 stars 1 rating. See all 3 formats and editions Hide other formats and editions. Amazon Price 1/5(1). This book offers an introduction to the theory of differentiable manifolds and fiber bundles.

It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle.3/5(1).

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 MilnorBrand: Birkhäuser Basel.

This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle.

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century.

This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle/5(K).

Book IV continues the discussion begun in the first three volumes. Although it is aimed at first-year graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be accessible to undergraduates interested in affine differential geometry.

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.

In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian es have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsically, reflecting their properties determined solely by the.

Metric Structures in Differential Geometry. This text is aimed to be an elementary introduction to differential geometry. It consists of six Chapters. In Chapter 1 (“Differentiable manifolds”) the author treats, besides the standard results and concepts about manifolds, multilinear algebra and tensor fields as well as the de Rham cohomology.

Topics in Differential Geometry is a collection of papers related to the work of Evan Tom Davies in differential geometry. Some papers discuss projective differential geometry, the neutrino energy-momentum tensor, and the divergence-free third order concomitants of.

Natural Operations in Differential Geometry. This book is a monographical work on natural bundles and natural operators in differential geometry and this book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in different branches of differential geometry.

Abstract: “Metric geometry” is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations.

Buy Metric Structures in Differential Geometry by Gerard Walschap from Waterstones today! Click and Collect from your local Waterstones or get FREE UK delivery on orders over £Book Edition: Softcover Reprint of The Original 1st Ed. Books shelved as differential-geometry: Differential Geometry of Curves and Surfaces by Manfredo P.

Do Carmo, Topology and Geometry for Physicists by Cha.An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector fields with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion for further research.