A new approach on helices in pseudo-Riemannian manifolds. (English) Zbl 1474.53026

Zıplar, Evren; Yaylı, Yusuf; Gök, İsmail

Abstr. Appl. Anal. 2014, Article ID 718726, 6 p. (2014).

Summary: A proper curve \(\alpha\) in the \(n\)-dimensional pseudo-Riemannian manifold \((M, g)\) is called a \(V_n\)-slant helix if the function \(g(V_n, X)\) is a nonzero constant along \(\alpha\), where \(X\) is a parallel vector field along \(\alpha\) and \(V_n\) is \(n\)th Frenet frame. In this work, we study such curves and give important characterizations about them.

MSC:

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

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