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Curvature in Mathematics and Physics (Dover Books on Mathematics),New
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This original text for courses in differential geometry is geared toward advanced undergraduate and graduate majors in math and physics. Based on an advanced class taught by a worldrenowned mathematician for more than fifty years, the treatment introduces semiRiemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool.Starting with an introduction to the various curvatures associated to a hypersurface embedded in Euclidean space, the text advances to a brief review of the differential and integral calculus on manifolds. A discussion of the fundamental notions of linear connections and their curvatures follows, along with considerations of LeviCivita's theorem, biinvariant metrics on a Lie group, Cartan calculations, Gauss's lemma, and variational formulas. Additional topics include the HopfRinow, Myer's, and Frobenius theorems; special and general relativity; connections on principal and associated bundles; the star operator; superconnections; semiRiemannian submersions; and Petrov types. Prerequisites include linear algebra and advanced calculus, preferably in the language of differential forms.
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- Q: What is the main focus of 'Curvature in Mathematics and Physics'? A: The book primarily focuses on differential geometry, particularly semi-Riemannian geometry, and its applications in physics, especially Einstein's theory of general relativity.
- Q: Who is the author of this book? A: The author of 'Curvature in Mathematics and Physics' is Shlomo Sternberg, a renowned mathematician with extensive teaching experience.
- Q: What are the prerequisites for understanding this book? A: The prerequisites include a strong foundation in linear algebra and advanced calculus, preferably with knowledge of differential forms.
- Q: How many pages does the book have? A: The book contains a total of 416 pages.
- Q: What is the binding type of this book? A: This edition of the book is available in paperback binding.
- Q: When was 'Curvature in Mathematics and Physics' published? A: The book was published on September 19, 2012.
- Q: Is this book suitable for beginners in mathematics? A: No, this book is geared towards advanced undergraduate and graduate students, so it may not be suitable for beginners.
- Q: What topics are covered in 'Curvature in Mathematics and Physics'? A: Topics include linear connections, curvatures, the Hopf-Rinow theorem, special and general relativity, and variational formulas, among others.
- Q: Does this book include illustrations? A: Yes, this is an illustrated edition, which enhances the understanding of complex concepts.
- Q: What category does this book fall under? A: The book falls under the category of Differential Geometry.