By Loring W. Tu
ISBN-10: 3319550829
ISBN-13: 9783319550824
Prerequisite fabric is contained in author's text An creation to Manifolds, and will be discovered in a single semester. For the advantage of the reader and to set up universal notations, Appendix A remembers the fundamentals of manifold idea. also, in an try to make the exposition extra self-contained, sections on algebraic buildings reminiscent of the tensor product and the outside strength are included.
Differential geometry, as its identify implies, is the learn of geometry utilizing differential calculus. It dates again to Newton and Leibniz within the 17th century, however it was once now not till the 19th century, with the paintings of Gauss on surfaces and Riemann at the curvature tensor, that differential geometry flourished and its sleek starting place was once laid. during the last 100 years, differential geometry has confirmed quintessential to an figuring out of the actual global, in Einstein's common conception of relativity, within the idea of gravitation, in gauge concept, and now in string conception. Differential geometry can also be precious in topology, numerous advanced variables, algebraic geometry, advanced manifolds, and dynamical platforms, between different fields. The box has even came across purposes to team idea as in Gromov's paintings and to likelihood thought as in Diaconis's paintings. it's not too far-fetched to argue that differential geometry might be in each mathematician's arsenal.
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Differential Geometry: Connections, Curvature, and Characteristic Classes (Graduate Texts in Mathematics) by Loring W. Tu
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