This textbook offers a rigorous introduction to the foundations of Riemannian Geometry, with a detailed treatment of homogeneous and symmetric spaces, as well as the foundations of the General Theory of Relativity. Starting with the basics of manifolds, it presents key objects of differential geometry, such as Lie groups, vector bundles, and de Rham cohomology, with full mathematical details. Next, the fundamental concepts of Riemannian geometry are introduced, paving the way for the study of homogeneous and symmetric ...
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This textbook offers a rigorous introduction to the foundations of Riemannian Geometry, with a detailed treatment of homogeneous and symmetric spaces, as well as the foundations of the General Theory of Relativity. Starting with the basics of manifolds, it presents key objects of differential geometry, such as Lie groups, vector bundles, and de Rham cohomology, with full mathematical details. Next, the fundamental concepts of Riemannian geometry are introduced, paving the way for the study of homogeneous and symmetric spaces. As an early application, a version of the Poincar???-Hopf and Chern-Gauss-Bonnet Theorems is derived. The final chapter provides an axiomatic deduction of the fundamental equations of the General Theory of Relativity as another important application. Throughout, the theory is illustrated with color figures to promote intuitive understanding, and over 200 exercises are provided (many with solutions) to help master the material. The book is designed to cover a two-semester graduate course for students in mathematics or theoretical physics and can also be used for advanced undergraduate courses. It assumes a solid understanding of multivariable calculus and linear algebra.
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Add this copy of Differential Geometry and Homogeneous Spaces to cart. $65.23, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2024 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
Edition:
2024, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2024
Language:
English
Alibris ID:
18151763022
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