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.
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Spallek, K. Geometrische Bedingungen für die Integrabilität von Vektorfeldern auf Teilmengen des ℝn . Manuscripta Math 25, 147–160 (1978). https://doi.org/10.1007/BF01168606
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DOI: https://doi.org/10.1007/BF01168606