Contradictions in Differential Equations

  1. (Two different conventions should not be mixed up) Klingenberg's contradiction.
        [Kli, p.13, Proposition 1.3.4] states that for the distinguished Frenet-frame, ki(t) > 0. In [Kli, p.15, l.-4], Klingenberg claims that k(t) can be negative. The latter claim is incorrect. In fact, if we use the distinguished Frenet-frame, k(t) is always positive. Inclusion of the case k < 0 [Kli, p.16, Fig. 1.4] requires a more refined definition of curvature [Wea1, p.11, l.-7]. [Kli, p. 15, l.-2-l.-1] is the consequence of [Wea1, p.11, l.-7] rather than [Kli, p.15, l.-6]. See [Wea1, p.11, l.-6-p.13, l.1].

  2. Links {1}.