Claudio Gorodski: Smooth Manifolds

Cover: 9783030497743 | Smooth Manifolds | Claudio Gorodski | Taschenbuch | xii | Englisch

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Sprache: Englisch

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Beschreibung

This concise and practical textbook presents the essence of the theory on smooth manifolds. A key concept in mathematics, smooth manifolds are ubiquitous: They appear as Riemannian manifolds in differential geometry; as space-times in general relativity; as phase spaces and energy levels in mechanics; as domains of definition of ODEs in dynamical systems; as Lie groups in algebra and geometry; and in many other areas. The book first presents the language of smooth manifolds, culminating with the Frobenius theorem, before discussing the language of tensors (which includes a presentation of the exterior derivative of differential forms). It then covers Lie groups and Lie algebras, briefly addressing homogeneous manifolds. Integration on manifolds, explanations of Stokes¿ theorem and de Rham cohomology, and rudiments of differential topology complete this work. It also includes exercises throughout the text to help readers grasp the theory, as well as more advanced problems for challenge-oriented minds at the end of each chapter. Conceived for a one-semester course on Differentiable Manifolds and Lie Groups, which is offered by many graduate programs worldwide, it is a valuable resource for students and lecturers alike.

Über den Autor

Claudio Gorodski is a Full Professor at the Institute of Mathematics and Statistics, University of São Paulo, Brazil. He holds a PhD in Mathematics (1992) from the University of California at Berkeley, USA, and a Habilitation degree (1998) from the University of São Paulo, Brazil. His research interests include Lie transformation groups in Riemannian geometry, geometry of submanifolds, Riemannian symmetric spaces, and sub-Riemannian geometry.

Zusammenfassung

Presents the essence of the theory on smooth manifolds

Covers key topics such as submanifolds, tensor fields, Lie groups, integration (including Stokes' theorem and De Rham cohomology), as well as manifolds

Includes comprehension exercises throughout the text and challenging problems at the end of each chapter

Inhaltsverzeichnis

Preface.- Smooth manifolds.- Tensor fields and differential forms.- Lie groups.- Integration.- Appendix A: Covering manifolds.- Appendix B: Hodge Theory.- Bibliography.- Index.

Details

Erscheinungsjahr:	2020
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xii 154 S. 11 s/w Illustr. 154 p. 11 illus.
ISBN-13:	9783030497743
ISBN-10:	3030497747
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Gorodski, Claudio
Auflage:	1st edition 2020
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	235 x 155 x 9 mm
Von/Mit:	Claudio Gorodski
Erscheinungsdatum:	02.08.2020
Gewicht:	0,301 kg