Gerard Walschap's Books

Multivariable Calculus and Differential Geometry

By: Gerard Walschap

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Multivariable Calculus and Differential Geometry

By: Gerard Walschap

This book offers an introduction to differential geometry for the non-specialist. It includes most of the required material from multivariable calculus, linear algebra, and basic analysis. An intuitive approach and a minimum of prerequisites make it a valuable companion for students of mathematics and physics. The main focus is on manifolds in Euclidean space and the metric properties they inherit from it. Among the topics discussed are curvature and how it affects the shape of space, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.

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Page Count

366

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110369540

ISBN 13

9783110369540

Metric Structures in Differential Geometry

By: Gerard Walschap

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Metric Structures in Differential Geometry

By: Gerard Walschap

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. These concepts are illustrated in detail for bundles over spheres.

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Page Count

235

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387218262

ISBN 13

9780387218267

Metric Foliations and Curvature

By: Detlef Gromoll,Gerard Walschap

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Metric Foliations and Curvature

By: Detlef Gromoll,Gerard Walschap

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.

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