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Let M{\subset}\mathbb{R}^{n} be a Riemannian helix submanifold with respectto the unit direction d{\in}\mathbb{R}^{n} and f:M{\to}\mathbb{R} be a eikonalfunction. We say that M is a f-eikonal helix submanifold if for each q{\in}Mthe angle between {\nabla}f and d is constant.Let M{\subset}\mathbb{R}^{n} be aRiemannian submanifold and {\alpha}:I{\to}M be a curve with unit tangent T. Letf:M{\to}\mathbb{R} be a eikonal function along the curve {\alpha}. We say that{\alpha} is a f-eikonal helix curve if the angle between {\nabla}f and T isconstant along the curve {\alpha}. {\nabla}f will be called as the axis of thef-eikonal helix curve.The aim of this article is to give that the relationsbetween f-eikonal helix submanifolds and f-eikonal helix curves, and toinvestigate f-eikonal helix curves on Riemannian manifolds.

f-Eikonal helix submanifolds and f-Eikonal helix curves