Differential geometry : connections, curvature, and characteristic classes /: connections, curvature, and characteristic classes. (2017)

• Record Type: Book
• Further Information: Note: Loring W. Tu.
• Authors: Tu, Loring W
• Contents: Preface -- Chapter 1. Curvature and Vector Fields -- 1. Riemannian Manifolds -- 2. Curves -- 3. Surfaces in Space -- 4. Directional Derivative in Euclidean Space -- 5. The Shape Operator -- 6. Affine Connections -- 7. Vector Bundles -- 8. Gauss's Theorema Egregium -- 9. Generalizations to Hypersurfaces in Rn+1 -- Chapter 2. Curvature and Differential Forms -- 10. Connections on a Vector Bundle -- 11. Connection, Curvature, and Torsion Forms -- 12. The Theorema Egregium Using Forms -- Chapter 3. Geodesics -- 13. More on Affine Connections -- 14. Geodesics -- 15. Exponential Maps -- 16. Distance and Volume -- 17. The Gauss-Bonnet Theorem -- Chapter 4. Tools from Algebra and Topology -- 18. The Tensor Product and the Dual Module -- 19. The Exterior Power -- 20. Operations on Vector Bundles -- 21. Vector-Valued Forms -- Chapter 5. Vector Bundles and Characteristic Classes -- 22. Connections and Curvature Again -- 23. Characteristic Classes -- 24. Pontrjagin Classes -- 25. The Euler Class and Chern Classes -- 26. Some Applications of Characteristic Classes -- Chapter 6. Principal Bundles and Characteristic Classes -- 27. Principal Bundles -- 28. Connections on a Principal Bundle -- 29. Horizontal Distributions on a Frame Bundle -- 30. Curvature on a Principal Bundle -- 31. Covariant Derivative on a Principal Bundle -- 32. Character Classes of Principal Bundles -- A. Manifolds -- B. Invariant Polynomials -- Hints and Solutions to Selected End-of-Section Problems -- List of Notations -- References -- Index.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Extent: 1 online resource (xvii, 347 pages), illustrations (some color)
• Subjects: 516.3/6; Mathematics; Geometry, Differential; Global differential geometry; Geometry, algebraic; Geometry, Differential; Mathematics -- Geometry -- Algebraic; Algebraic geometry; Mathematics -- Geometry -- Differential; Differential & Riemannian geometry; Mathematics; Differential Geometry; Algebraic Geometry; Electronic books; Electronic book
• Languages: English
• ISBNs: 9783319550848; 3319550845; 3319550829; 9783319550824
• Related ISBNs: 9783319550824
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed June 5, 2017).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.