jumble
发表于 2025-3-23 13:05:19
Differentiable Manifoldsoncepts connected with the notion of a differentiable manifold. We give two definitions of a differentiable manifold. The standard one starts with a topological space. One can alternatively begin with a set and introduce the topology with a given atlas. This approach is not only practical to constru
CLOT
发表于 2025-3-23 15:15:32
Tangent Vectors, Vector and Tensor Fieldsfinitions. On the basis this notion vector fields are introduced, together with their Lie algebra structure. In the subsection on tensor fields, the reader is assumed to be familiar with some basic material of multilinear algebra. Important examples of tensor fields are (pseudo-) Riemannian metrics
原来
发表于 2025-3-23 21:03:18
http://reply.papertrans.cn/39/3822/382107/382107_13.png
冷淡周边
发表于 2025-3-24 00:44:23
Differential Forms repeating some algebraic preliminaries on exterior algebras. Then exterior differential forms and the associated exterior algebra are introduced. On this we study general properties of derivations and antiderivations. The most important one is Cartan’s exterior derivative. Poincaré’s Lemma is also
联想
发表于 2025-3-24 05:25:52
http://reply.papertrans.cn/39/3822/382107/382107_15.png
使坚硬
发表于 2025-3-24 08:43:45
Some Details and Supplementslong maps and their induced covariant derivatives, because this is used at various places in the book. For a convenient formulation we introduce the tangent bundle of a manifold, the prototype of a vector bundle. Applications to variations of curves will illustrate the usefulness of the concepts.
细丝
发表于 2025-3-24 13:16:02
http://reply.papertrans.cn/39/3822/382107/382107_17.png
消息灵通
发表于 2025-3-24 17:43:27
http://reply.papertrans.cn/39/3822/382107/382107_18.png
厨师
发表于 2025-3-24 21:38:09
Interpreting the Chemical Residues Storyly to the kinematical framework of GR and determines—suitable interpreted—the coupling of physical systems to external gravitational fields. This is discussed in detail in the present chapter. Although Einstein’s Equivalence Principle (EEP) is somewhat vague, since it is not entirely clear what is m
manifestation
发表于 2025-3-25 00:42:34
https://doi.org/10.1007/3-540-30571-8r, we shall first give a simple physical motivation for the field equation and will then show that it is determined by only a few natural requirements (Lovelock theorem), with two coupling constants. One is just Newtons gravitational constant, and the other is the much discussed cosmological constan