000			02249nam a22002417a 4500
008			240708b |||||||| |||| 00| 0 eng d
020			_a9783319855622 (PB)
041			_aeng
080			_a514.7 _bTUL
100			_aTu, Loring W.
245			_aDifferential Geometry _b: Connections, Curvature, and Characteristic Classes
260			_aCham _bSpringer _c2017
300			_axvi, 346p. _bill.
490			_aGraduate Texts in Mathematics _v275
504			_aIncludes References (335-336) and Index
505			_a1. Curvature and Vector Fields 2. Curvature and Differential Forms 3. Geodesics 4. Tools from Algebra and Topology 5. Vector Bundles and Characteristic Classes 6. Principal Bundles and Characteristic Classes
520			_aThis text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus.
650			_aRiemannian geometry
650			_aGeodesics
650			_aDifferential Forms
690			_aMathematics
942			_cBK
999			_c60513 _d60513