Differential geometry: bundles, connections, metrics and curvature
Taubes, Clifford Henry
Differential geometry: bundles, connections, metrics and curvature - Oxford: Oxford University Press, 2011. - xiii, 298 p.: pbk.: 23 cm. - Oxford Graduate Texts in Mathematics; 23 .
Includes Index
Bundles, connections, metrics, and curvature are the ‘lingua franca’ of modern differential geometry and theoretical physics. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the definition of characteristic classes, and also an introduction to complex and Kähler geometry. The book uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life.
https://academic.oup.com/book/12200
9780198961550
Mathematics
Geometry
Analytic Geometry
Differential and Integral Geometry
Differential Topology
Differentiable Manifolds
516.36 TAU
Differential geometry: bundles, connections, metrics and curvature - Oxford: Oxford University Press, 2011. - xiii, 298 p.: pbk.: 23 cm. - Oxford Graduate Texts in Mathematics; 23 .
Includes Index
Bundles, connections, metrics, and curvature are the ‘lingua franca’ of modern differential geometry and theoretical physics. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the definition of characteristic classes, and also an introduction to complex and Kähler geometry. The book uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life.
https://academic.oup.com/book/12200
9780198961550
Mathematics
Geometry
Analytic Geometry
Differential and Integral Geometry
Differential Topology
Differentiable Manifolds
516.36 TAU
