Smarandache curves according to curves on a spacelike surface in Minkowski 3-space \(\mathbb R^3_1\). (English) Zbl 1305.53015

Ozturk, Ufuk; Ozturk, Esra Betul Koc

J. Discrete Math. 2014, Article ID 829581, 10 p. (2014).

Summary: We introduce Smarandache curves according to the Lorentzian Darboux frame of a curve on a space-like surface in Minkowski 3-space \(\mathbb R^3_1\). Also, we obtain the Sabban frame and the geodesic curvature of the Smarandache curves and give some characterizations on the curves when the curve \(\alpha \) is an asymptotic curve or a principal curve. And we give an example to illustrate these curves.

MSC:

53A35	Non-Euclidean differential geometry
53B30	Local differential geometry of Lorentz metrics, indefinite metrics
53A04	Curves in Euclidean and related spaces

Keywords:

Sabban frame; geodesic curvature

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