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Lectures on the geometry of manifolds [electronic resource] / by Liviu I. Nicolaescu.

By: Nicolaescu, Liviu I.
Material type: materialTypeLabelBookPublisher: Singapore : World Scientific, 2020Edition: 3rd. ed.Description: 1 online resource (xviii, 682 p.).ISBN: 9789811214820.Subject(s): Geometry, Differential | Manifolds (Mathematics)Genre/Form: Electronic books.DDC classification: 516.362 Online resources: Access to full text is restricted to subscribers.
Contents:
Manifolds -- Natural constructions on manifolds -- Calculus on manifolds -- Riemannian geometry -- Elements of the calculus of variations -- The fundamental group and covering spaces -- Cohomology -- Characteristic classes -- Classical integral geometry -- Elliptic equations on manifolds -- Spectral geometry -- Dirac operators.
Summary: "The goal of this book is to introduce the reader to some of the main techniques, ideas and concepts frequently used in modern geometry. It starts from scratch and it covers basic topics such as differential and integral calculus on manifolds, connections on vector bundles and their curvatures, basic Riemannian geometry, calculus of variations, DeRham cohomology, integral geometry (tube and Crofton formulas), characteristic classes, elliptic equations on manifolds and Dirac operators. The new edition contains a new chapter on spectral geometry presenting recent results which appear here for the first time in printed form"--Publisher's website.
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"The goal of this book is to introduce the reader to some of the main techniques, ideas and concepts frequently used in modern geometry. It starts from scratch and it covers basic topics such as differential and integral calculus on manifolds, connections on vector bundles and their curvatures, basic Riemannian geometry, calculus of variations, DeRham cohomology, integral geometry (tube and Crofton formulas), characteristic classes, elliptic equations on manifolds and Dirac operators. The new edition contains a new chapter on spectral geometry presenting recent results which appear here for the first time in printed form"--Publisher's website.

Manifolds -- Natural constructions on manifolds -- Calculus on manifolds -- Riemannian geometry -- Elements of the calculus of variations -- The fundamental group and covering spaces -- Cohomology -- Characteristic classes -- Classical integral geometry -- Elliptic equations on manifolds -- Spectral geometry -- Dirac operators.

Includes bibliographical references and index.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

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