2012/06/02 by Evren Ziplar, Ziplar, Evren, Ali Senol +3
Mathematics · #53A04 #53B25 #53C40 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A04 #msc:53B25 #msc:53C40 #msc:53C50
paper · pdf · doi:10.48550/arxiv.1206.0395
arXiv admin note: text overlap with arXiv:1205.2186
arxiv created 2012/12/05 · arxiv updated 2012/12/06
Let M⊂ℝn be a Riemannian helix submanifold with respect to the unit direction d∈ℝn and f:M→ℝ be a eikonal function. We say that M is a f-eikonal helix submanifold if for each q∈M the angle between ∇f and d is constant.Let M⊂ℝn be a Riemannian submanifold and α:I→M be a curve with unit tangent T. Let f:M→ℝ be a eikonal function along the curve α. We say that α is a f-eikonal helix curve if the angle between ∇f and T is constant along the curve α. ∇f will be called as the axis of the f-eikonal helix curve.The aim of this article is to give that the relations between f-eikonal helix submanifolds and f-eikonal helix curves, and to investigate f-eikonal helix curves on Riemannian manifolds.