Closed Integral Curves in 3-space and Isotopic Two-dimensional Deformations
نویسنده
چکیده
If there is given an isotopic deformation of a two-dimensional euclidean plane E onto itself, one can adjoin to every point P of E a certain closed curve, the so-called "indicatrix" of P (§1). If the indicatrix does not pass through P, we introduce the order of P relative to its indicatrix as the "rotation number" of the deformation at P. A relation between the rotation numbers in different points of E (§3) and a formula for the rotation number in the general case of a "bounded deformation" (§4) is established. This formula admits an application to the problem of closed integral curves of continuous vector fields in the 3-dimensional sphere.
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