Slant curves in the Lorentzian warped product manifold - I× fE²

Abstract

In this work, we study slant curves in the 3-dimensional Lorentzian warped product - I× fE², where E² is a 2-dimensional Euclidean plane, I? R is an open interval equipped with the metric dt², and f is a positive smooth function on I. First we give a characterization of slant curves, and then we obtain a classification of all slant curves in - I× fE². We also compute their curvature and torsion, and we obtaine some results on slant curves and helices in the de Sitter space S13(1) and in the Minkowski space E13. Moreover we determined some biharmonic slant curves in S13(1).