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arXiv · 1601.02992

Zero sets of Abelian Lie algebras of vector fields

Morris W. Hirsch
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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.

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Morris W. Hirsch. 2016-01-12. Zero sets of Abelian Lie algebras of vector fields. https://arxiv.org/abs/1601.02992

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