Zero sets of Abelian Lie algebras of vector fields
Dynamical Systems
2016-01-13 v1
Abstract
Assume M is a 3-dimensional real manifold without boundary, A is an abelian Lie algebra of analytic vector fields on M, and X is an element of A. The following result is proved: If K is a locally maximal compact set of zeroes of X and the Poincar'e-Hopf index of X at K is nonzero, there is a point in K at which all the elements of A vanish.
Keywords
Cite
@article{arxiv.1601.02992,
title = {Zero sets of Abelian Lie algebras of vector fields},
author = {Morris W. Hirsch},
journal= {arXiv preprint arXiv:1601.02992},
year = {2016}
}
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8 pages