Shlomo Sternberg

Curvature in Mathematics and Physics

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Dover Books on Mathema 1.4tics
• Verlag: Dover Publications Inc.
• Seitenzahl: 416
• Erscheinungstermin: 26. Oktober 2012
• Englisch
• Abmessung: 233mm x 158mm x 22mm
• Gewicht: 588g
• ISBN-13: 9780486478555
• ISBN-10: 0486478556
• Artikelnr.: 34558486

Autorenporträt

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.

Inhaltsangabe

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