Characterizations of slant helices in Euclidean 3-space

In this paper we investigate the relations between a general helix and a slant helix. Moreover, we obtain some differential equations which they are characterizations for a space curve to be a slant helix. Also, we obtain the slant helix equations and its Frenet aparatus.

Characterizations of slant helices in Euclidean 3-space

In this paper we investigate the relations between a general helix and a slant helix. Moreover, we obtain some differential equations which they are characterizations for a space curve to be a slant helix. Also, we obtain the slant helix equations and its Frenet aparatus.

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  • (b) Figure 3. The slant helices for c =±1 (a) and tangent indicatricies of the slant helices for c = ±1 (b) (a)
  • (b) Figure 4. The slant helices for c =±4 (a) and tangent indicatricies of the slant helices for c = ±4 (b) (a)
  • (b) Figure 5. The slant helices for c =±6 (a) and tangent indicatricies of the slant helices for c = ±6 (b)