A note on helices in the Euclidean space and in the hyperbolic space

Abstract We prove that general helices in Euclidean space for Killing vector fields associated to rotations are helices, that is, curves with constant curvature and constant torsion. In hyperbolic space $${\mathbb {H}}^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> , we obtain the parametrizations of helices for all types of Killing vector fields. It is proved that these helices are geodesics in suitable surfaces of $${\mathbb {H}}^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> .