Geometrische Bedingungen für die Integrabilität von Vektorfeldern auf Teilmengen des ℝⁿ

Abstract

We give a geometric characterisation for those vectorfields on a subset X ⊂ ℝⁿ, wich are locally integrable, that is, which locally have sufficiently many integral curves on X. From this we deduce, that integrable spaces X (where each field of a fixed class of differentiability is locally integrable) are rigid under differentiable deformations in the sense of Kodaira-Kuranishi. We give a general construction for integrable spaces and obtain, that analytic varieties induce integrable spaces for each class of differentiability. Compact analytic varieties are therefore C^∞-rigid, which extends [4], 3,1.