Eikonal slant helices and eikonal Darboux helices in 3-dimensional pseudo-Riemannian manifolds

2013/10/25 by Mehmet Önder, Önder, Mehmet, Evren Ziplar +1
Mathematics · #53B40 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53B40 #msc:53C50

paper · pdf · doi:10.48550/arxiv.1310.7015

arXiv admin note: substantial text overlap with arXiv:1310.6931

arxiv created 2013/10/25 · arxiv updated 2013/10/29

Abstract

In this study, we give definitions and characterizations of eikonal slant helices, eikonal Darboux helices and non-normed eikonal Darboux helices in 3-dimensional pseudo- Riemannian manifold M . We show that every eikonal slant helix is also an eikonal Darboux helix for timelike and spacelike curves. Furthermore, we obtain that if the non-null curve a is a non-normed eikonal Darboux helix, then a is an eikonal slant helix if and only if 2 2 e 3k +e1t = constant, where k and t are curvature and torsion of a, respectively. Finally, we define null-eikonal helices, slant helices and Darboux helices. Also, we give their characterizations.

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