Foliating Metric Spaces
度量几何
2007-05-23 v1 最优化与控制
摘要
Using families of curves to generalize vector fields, the Lie bracket is defined on a metric space, M. For M complete, versions of the local and global Frobenius theorems hold, and flows are shown to commute if and only if their bracket is zero. An example is given showing separable Hilbert space (the set of square integrable functions on R) is controllable by two elementary flows.
引用
@article{arxiv.math/0608416,
title = {Foliating Metric Spaces},
author = {Craig Calcaterra},
journal= {arXiv preprint arXiv:math/0608416},
year = {2007}
}
备注
37 pages, 3 figures