A note on (n - r)-curvature planes

Abstract

After introducing the notions of i-th e-curvature (or m<inf>i</inf>- curvature) function, r-th (a<inf>1</inf>,..., a<inf>r</inf>)-curvature center and (n - r)-curvature plane for Euclidean space curves, it is proved that the locus of centers of the spheres having an r-multiple contact point with the curve is the associated (n - r)-curvature plane. Particular examples are provided as well.