Smooth Manifolds. 1st ed. 2020

種類:

電子ブック

責任表示:

by Claudio Gorodski

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2020

著者名:

• Gorodski, Claudio.
• SpringerLink (Online service)

シリーズ名:

Compact Textbooks in Mathematics ;

ISBN:

9783030497750 [3030497755]    

注記:

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

ローカル注記:

学内専用E-BOOKS (local access only)