Abstract
For such curves we know a moving frame and a complete system of invariants (affine curvatures) with respect to the group of volume-conserving transformations (unimodular group) of the order 2n−1 respectively 2n (see [1], p. 171). In this paper we study for a curvec a moving frame and a system of invariants of the minimal ordern+1, respectivelyn+2, by means of a curve with vanishing affine curvatures that has contact of maximal order withc. Forn=3 this is a result ofA. Winternitz ([1], p. 171 or [3], p. 86).
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Literatur
Guggenheimer, H.: Differential Geometry. New York: Inc. McGraw-Hill Book Company. 1963.
Paukowitsch, H.: Zur Kurventheorien-dimensionaler affiner Räume. Sb. Akad. Wiss. Wien. (Im Druck.)
Schirokow, P. u. A.: Affine Differentialgeometrie. Leipzig: Teubner. 1962.
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Paukowitsch, H.P. Begleitfiguren und Invariantensystem minimaler Differentiationsordnung von Kurven im reellenn-dimensionalen affinen Raum. Monatshefte für Mathematik 85, 137–148 (1978). https://doi.org/10.1007/BF01297543
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DOI: https://doi.org/10.1007/BF01297543