An Introduction to Riemannian Geometry With Applications to Mechanics and Relativity /

• Κύριοι συγγραφείς: Godinho, Leonor (Συγγραφέας), Natário, José (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Σειρά: Universitext,
• Θέματα: Mathematics.; Differential geometry.; Mathematical physics.; Gravitation.; Mechanics.; Differential Geometry.; Mathematical Physics.; Classical and Quantum Gravitation, Relativity Theory.
• Φυσική περιγραφή: X, 467 p. 60 illus. online resource.
• ISBN: 9783319086668
• ISSN: 0172-5939

Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.