Journal of Lie Theory

no. 4
Zero Sets of Abelian Lie Algebras of Vector Fields
Journal of Lie Theory, Volume 27 (2017) no. 4, pp. 907-914
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.
Theorem. If K is a locally maximal compact set of zeroes of X and the Poincaré-Hopf index of X at K is nonzero, there is a point in K at which all the elements of A vanish.
DOI: 10.5802/jolt.974
Classification: 37C10, 37C35
Keywords: Analytic vector field, real manifold, abelian Lie algebra 
@article{JOLT_2017_27_4_a0,
     author = {M. W. Hirsch},
     title = {Zero {Sets} of {Abelian} {Lie} {Algebras} of {Vector} {Fields}},
     journal = {Journal of Lie Theory},
     pages = {907--914},
     year = {2017},
     volume = {27},
     number = {4},
     doi = {10.5802/jolt.974},
     zbl = {1387.37024},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.974/}
}
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M. W. Hirsch. Zero Sets of Abelian Lie Algebras of Vector Fields. Journal of Lie Theory, Volume 27 (2017) no. 4, pp. 907-914. doi: 10.5802/jolt.974

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