虚度
发表于 2025-3-23 09:58:01
http://reply.papertrans.cn/16/1554/155328/155328_11.png
牌带来
发表于 2025-3-23 13:56:02
http://reply.papertrans.cn/16/1554/155328/155328_12.png
Comedienne
发表于 2025-3-23 21:02:32
,Die ideale moderne Universität,Intuitively, a manifold is a generalization of curves and surfaces to arbitrary dimension. While there are many different kinds of manifolds—topological manifolds, .-manifolds, analytic manifolds, and complex manifolds, in this book we are concerned mainly with smooth manifolds.
Brittle
发表于 2025-3-23 22:55:01
,Die ideale moderne Universität,Using coordinate charts we can transfer the notion of differentiability from R. to a smooth manifold ..
gospel
发表于 2025-3-24 05:11:08
http://reply.papertrans.cn/16/1554/155328/155328_15.png
Petechiae
发表于 2025-3-24 09:25:55
Die Universitäts-Hautklinik MünsterIn this chapter we analyze the local structure of a smooth map on the basis of its rank. Recall that the rank of a smooth map . : . → . at a point . ∈ . is the rank of its differential at .. Two cases are of special interest: when the map . has maximal rank at a point or constant rank in a neighborhood. Let . = dim . and . = dim..
modifier
发表于 2025-3-24 12:22:01
Anlagebedingte HauterkrankungenCertain manifolds such as the circle have in addition to their . structure also a group structure; moreover, the group operations are .∞. Manifolds such as these are called Lie groups. This chapter is a compendium of a few important examples of Lie groups, the ..
轮流
发表于 2025-3-24 18:46:24
http://reply.papertrans.cn/16/1554/155328/155328_18.png
投票
发表于 2025-3-24 21:36:37
Alternating k-Linear FunctionsThis chapter is purely algebraic. Its purpose is to develop the properties of alternating .-linear functions on a vector space for later application to the tangent space at a point of a manifold.
needle
发表于 2025-3-25 00:21:32
http://reply.papertrans.cn/16/1554/155328/155328_20.png