This study analyses (k,m)-type slant helices in compliance with the modified orthogonal frame 3-dimensional Euclidean space ($\mathbb{E}^{3}$). Furthermore, we perform some characterisations of curves frames $\mathbb{E}^{3}$.

In this work, the notion of a slant helix is extended to the space E. First, we introduce the type-2 harmonic curvatures of a regular curve. Thereafter, by using this, we present some necessary and sufficient conditions for a curve to be a slant helix in Euclidean n-space. We also express some integral characterizations of such curves in terms of the curvature functions. Finally, we give some c...

We consider a unit speed curve α in Euclidean four-dimensional space E and denote the Frenet frame by {T,N,B1,B2}. We say that α is a slant helix if its principal normal vector N makes a constant angle with a fixed direction U . In this work we give different characterizations of such curves in terms of their curvatures. MSC: 53C40, 53C50

Inclined curves or so-called general helices are well-known curves in the classical differential geometry of space curves [9] and we refer to the reader for recent works on this type of curves [6, 12]. Recently, Izumiya and Takeuchi have introduced the concept of slant helix in Euclidean 3-space E saying that the normal lines makes a constant angle with a fixed direction [7]. They characterize ...

We consider a curve α = α(s) in Minkowski 3-space E31 and denote by {T,N,B} the Frenet frame of α. We say that α is a slant helix if there exists a fixed direction U of E31 such that the function 〈N(s), U〉 is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of α. MSC: 53C40, 53C50