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

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.


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