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تسجيل مستخدم جديدZero sets of Lie algebras of analytic vector fields on real and complex 2-manifolds
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تأليف
Morris W. Hirsch
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Let X be an analytic vector field on a real or complex 2-manifold, and K a compact set of zeros of X whose fixed point index is not zero. Let A denote the Lie algebra of analytic vector fields Y on M such that at every point of M the values of X and [X,Y] are linearly dependent. Then the vector fields in A have a common zero in K. Application: Let G be a connected Lie group having a 1-dimensional normal subgroup. Then every action of G on M has a fixed point.
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On a real ($mathbb F=mathbb R$) or complex ($mathbb F=mathbb C$) analytic connected 2-manifold $M$ with empty boundary consider two vector fields $X,Y$. We say that $Y$ {it tracks} $X$ if $[Y,X]=fX$ for some continuous function $fcolon Mrightarrowmat
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