如果一个人第一次见到哪怕只是二维球面S2的切丛T(S2)和余切丛T∗(S2)，那这种几何对象对他来说也...
Minimally Immersed Klein Bottles in the Unit Tangent Bundle of the Unit 2-Sphere Arising from Area-Minimizing Unit Vector Fields on S2\\{N,S}doi:10.1007/s12220-023-01190-4KLEIN bottlesVECTOR fieldsALGEBRAIC field theoryMINIMAL surfacesMATHEMATICSArea-minimizing unit vector...
S2上所有点的切平面全体构成了一个bundle 模掉原点相同这个等价关系得到的商空间就是这个bundle的底也就...
s2(x, y, z, p, q, r) = ((x, y, z), (x, y, p, q)) 2 (These morphisms are defined globally also: for the details cf. [1]). Let h1 and h2 be the inverses of the isomorphisms V π1(T2M) −→ T2M ×M TM
A simple example of a nontrivial tangent bundle is that of the unit sphere S2: this tangent bundle is nontrivial as a consequence of the hairy ball theorem. Therefore, the sphere is not parallelizable.Vector fieldsA smooth assignment of a tangent vector to each point of a manifold is ...
For these unit vector fields with even Poincaré indexes, we prove that the topological closure of their image coincides with the image of minimally immersed Klein bottles inT1S2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{...
如果一个人第一次见到哪怕只是二维球面S2的切丛T(S2)和余切丛T∗(S2)，那这种几何对象对他来说也...
，并形成基于原流形两倍维度的微分流形（differentiable manifold），称之流形的切丛（tangent bundle）。
流形上每一个点都有一个切空间TpM，将所有点的切空间收集起来就称为M的tangent bundle；如果在每一点...
谢 @叶修宜邀。见下图 （John W. Milnor and James D. Stasheff,Characteristic Classes,page 6）...