Geodesic
Zero Sets of Abelian Lie Algebras of Vector Fields
Morris W. Hirsch1
1Department of Mathematics, University of Wisconsin, 7926 Albe Road, Cross Plains, WI 53528, U.S.A.
Journal of Lie Theory, Tome 27 (2017) no. 4, pp. 907-914

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 37C10, 37C35
Mots-clés : Analytic vector field, real manifold, abelian Lie algebra

Morris W. Hirsch  1

1 Department of Mathematics, University of Wisconsin, 7926 Albe Road, Cross Plains, WI 53528, U.S.A. 
Morris W. Hirsch. Zero Sets of Abelian Lie Algebras of Vector Fields. Journal of Lie Theory, Tome 27 (2017) no. 4, pp. 907-914. http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a0/
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     title = {Zero {Sets} of {Abelian} {Lie} {Algebras} of {Vector} {Fields}},
     journal = {Journal of Lie Theory},
     pages = {907--914},
     year = {2017},
     volume = {27},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a0/}
}
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