健谈的人
发表于 2025-3-28 15:19:40
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伦理学
发表于 2025-3-28 22:38:43
,Stokes’ Theorem,If . is a manifold and . a submanifold, then any differential form on . induces a form on .. We can view this as a very special case of the inverse image of a form, under the embedding (injection) map.
Medley
发表于 2025-3-29 01:56:05
Differential Calculus,my book on real analysis give a self-contained and complete treatment for Banach spaces. We summarize certain facts concerning their properties as topological vector spaces, and then we summarize differential calculus. . and start immediately with Chapter II if the reader is accustomed to th
粘
发表于 2025-3-29 05:10:16
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我不死扛
发表于 2025-3-29 07:29:28
Vector Bundles,al glueing procedure can be used to construct more general objects known as vector bundles, which give powerful invariants of a given manifold. (For an interesting theorem see Mazur .) In this chapter, we develop purely formally certain functorial constructions having to do with vector bundl
machination
发表于 2025-3-29 13:03:22
Operations on Vector Fields and Differential Forms,g forms.” Applying it to the tangent bundle, we call the sections of our new bundle differential forms. One can define formally certain relations between functions, vector fields, and differential forms which lie at the foundations of differential and Riemannian geometry. We shall give the basic sys
腐蚀
发表于 2025-3-29 19:13:09
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Atheroma
发表于 2025-3-29 21:25:04
Covariant Derivatives and Geodesics,ssumed to be C. unless otherwise specified. We let X be a manifold. We denote the .-vector space of vector fields by ΓT(X). Observe that ΓT(X) is also a module over the ring of functions.We let π:TX →Xbe the natural map of the tangent bundle onto X.
magnate
发表于 2025-3-30 00:02:18
Volume Forms,ose extension to the infinite dimensional case is not evident. So this chapter is devoted to these forms of maximal degree. In the next chapter, we shall study how to integrate them, so the present chapter also provides a transition from the differential theory to the integration theory.
拱形大桥
发表于 2025-3-30 04:13:17
,Applications of Stokes’ Theorem,the computation of the maximal de Rham cohomology (the space of all forms of maximal degree modulo the subspace of exact forms); some come from Riemannian geometry; and some come from complex manifolds, as in Cauchy’s theorem and the Poincaré residue theorem. I hope that the selection of topics will