Curvature in Mathematics and Physics

Informationen zum Autor Shlomo Zvi Sternberg is a leading mathematician noted for his work in geometry. A longtime mathematics professor at Harvard University, he has written several textbooks for undergraduate students as well as a number of monographs used at Harvard and other educational institutions. Klappentext Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition. Inhaltsverzeichnis Introduction 1. Gauss's Theorem Egregium 2. Rules of Calculus 3. Connections on the Tangent Bundle 4. Levi-Civita's Theorem 5. Bi-invariant Metrics on a Lie Group 6. Cartan Calculations 7. Gauss's Lemma 8. Variational Formulas 9. The Hopf-Rinow Theorem 10. Curvature, Distance and Volume 11.Review of Special Relativity 12. The Star Operator and Electromagnetism 13. Preliminaries to the Einstein Equation 14. Die Grundlagen der Physik 15. The Frobenius Theorem 16. Connections on Principal Bundles 17. Reduction of Principal Bundles 18. Superconnections 19. Semi-Riemannian Submersions Bibliography Index

Klappentext
Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

Inhalt
Introduction 1. Gauss's Theorem Egregium 2. Rules of Calculus 3. Connections on the Tangent Bundle 4. Levi-Civita's Theorem 5. Bi-invariant Metrics on a Lie Group 6. Cartan Calculations 7. Gauss's Lemma 8. Variational Formulas 9. The Hopf-Rinow Theorem 10. Curvature, Distance and Volume 11.Review of Special Relativity 12. The Star Operator and Electromagnetism 13. Preliminaries to the Einstein Equation 14. Die Grundlagen der Physik 15. The Frobenius Theorem 16. Connections on Principal Bundles 17. Reduction of Principal Bundles 18. Superconnections 19. Semi-Riemannian Submersions Bibliography Index

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