Aspects of Differential Geometry II

Language: English

Published by Springer, 2015

3031012801 / 9783031012808

Series: Book 15 of 72 - Synthesis Lectures on Mathematics & Statistics

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Druck auf Anfrage Neuware - Printed after ordering - Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology ofcompact Lie groups and the Peter--Weyl Theorem are treated. In Chapter 7, material concerning homogeneous spaces and symmetric spaces is presented. Book II concludes in Chapter 8 where the relationship between simplicial cohomology, singular cohomology, sheaf cohomology, and de Rham cohomology is established. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the total curvature and length of curves given by a single ODE is new as is the discussion of the total Gaussian curvature of a surface defined by a pair of ODEs.

Seller Inventory # 9783031012808

Title
Aspects of Differential Geometry II
Author
Peter Gilkey
Publisher
Springer
Publication year
2015
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3031012801
ISBN 13
9783031012808
Item weight
312 grams
Dimensions
235x191x9 mm
Series
Book 15 of 72: Synthesis Lectures on Mathematics & Statistics

AHA-BUCH GmbH

Einbeck, Germany

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