Foliating Metric Spaces

Details Foliating Metric Spaces Foliating Metric Spaces

2006-08-16

arxiv.org/abs/math/0608416v1

Mathematics

Metric Geometry

37 pages, 3 figures

Scientific paper

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.

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