A Tour of Subriemannian Geometries, Their Geodesics and Applications
A Tour of Subriemannian Geometries, Their Geodesics and Applications
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DOI：
10.1090/surv/091
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发表时间：
2006-01
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影响因子：
--
通讯作者：
R. Montgomery
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文献类型：
--
作者：
R. Montgomery
次黎曼流形中的测地线：Dido meets Heisenberg Chow's theorem：Getting from A to B一条显著的水平曲线曲率和幂零奇异曲线和测地线分布的动物园Cartan's approach切锥和卡诺群倾向于卡诺几何的离散群未解决问题力学和丛的几何：杨-米尔斯场中的经典粒子量子相下落、游动和轨道运行几何力学丛与霍普夫纤维化Sussmann和Ambrose-Singer定理端点映射的微积分和测地线的存在性。
Geodesics in subriemannian manifolds: Dido meets Heisenberg Chow's theorem: Getting from A to B A remarkable horizontal curve Curvature and nilpotentization Singular curves and geodesics A zoo of distributions Cartan's approach The tangent cone and Carnot groups Discrete groups tending to Carnot geometries Open problems Mechanics and geometry of bundles: Metrics on bundles Classical particles in Yang-Mills fields Quantum phases Falling, swimming, and orbiting Appendices: Geometric mechanics Bundles and the Hopf fibration The Sussmann and Ambrose-Singer theorems Calculus of the endpoint map and existence of geodesics Bibliography Index.