黎曼幾何筆記 習作簿
Topics :
- 3-sphere
- Killing
fields
- Jacobi
fields
- Minimal
Surface
- Surface
of revolution
- Torus] [Geodesics]
- Spinning
Top Euler-Lagrange
equation(1) 用 Euler-Lagrange equation[R.Herman]
求geodesic equation and Christoffel symbols
- [Ricci---curvatrer
flow solitons]
- [Comparison
theorem]
第一章 向量場
[Topological
manifolds] [RG01 Jose Natario 第一章
習作]
[黎曼幾何簡介]
3.4.3節 Schwarzschild metric
第二章 微分式(Differential forms)
[RG01 Jose Natario 第二章
習作]
第三章 黎曼流形
[002
Cartan formalism]
有(1) p.18 把旋轉曲面看成IxS 求得 K Ric and R (2) p.19 先算IxS^2 再會去算p.22
S^3 (3) p.23 H^3 p.35 H^3 by Ivo
Terek Couto
[RG01
Jose Natario 第三章 習作]
[KillingandJacobi]
- Gauss-Bonnet theorem [Gauss
Bonnet Chern theorem] by Yin
Li
- 幾何與廣義相對論中的純量曲率
Richard(Rick) Schoen [專訪]
[Yamabe問題與正質量問題]
- [Spacetime and Geometry 第三章
Curvature] 第四章
[Gravitation]
[習作 and Answers] Sean
M. Carroll 1966- [ResearchGate]
[RG01 Jose Natario 第四章
習作] [Curvature
of IS^2] [Ricci curvature]
[Isotropic] [Exam2020]
[RicciSoliton]里奇孤子
[Sine-Gordon equation]
第五章 幾何力學
第六章 重力場
第七章 變分法
第八章 李群
[Lie
groups] 一個電腦資訊科學家的微分幾何與李群筆記 Jean
Gallier [Jean
Gallier] 這裡有很多書
第九章 向量叢
第十章 CMC曲面
[CMC曲面]
- An Introduction to Riemannian Geometry Jose Natario
- Riemannian Geometry Manfredo
P. do Carmo
- Spacetime and Geometry Sean Carroll [ProfoundPhysics]
[Spacetime and
Geometry(Exercises)]
- 物理學家用微分幾何 侯伯元 侯伯宇 檔名 DGforP
- Differential Geometry in Physics Gabriel
Lugo [ResearchGate]
- Geometry of Manifolds Richard L.Bishop
- Lectures on Geometry of Manifolds Liviu I. Nicolaescu
- 大域微分幾何 黃武雄
- 微分幾何講義 陳省身
- Differental Geometry 杜武亮
- An Introduction to Manifolds 杜武亮
- Differential Forms and Connections] Richard
W.R. Darling
- Riemannian
Geometry Peter
Petersen
- Differential
Forms for Physics Students William
O. Straub
- A course in modern mathematical physics Peter Szekeres
- Differential Geometry with Application to Mechanics and Physics Yves Talpaert
- Mathematical physics : Classical Mechanics Andreas Kmauf
- Differential forms with applications to the physical sciences Harley Flanders
- A Course in Differential Geometry
by Thierry Aubin
(1942~2009) Yamabe
problem
- 教科書/參考書書評
[Books] [Differential
Geometry論壇]