In this paper, the invariants of Smarandache curves, which consist Frenet vectors involute curve, are calculated in terms evolute curve.

Equiform geometry is considered an extension of other geometries. Furthermore, equiform frame a generalization the Frenet frame. In this study, we begin by defining term “equiform parameter (EQP)”, frame”, and formulas (EQF)” in regard to Minkowski three-space. Second, define spacelike normal curves (SPN) three-space present variety descriptions these with (EQS) or timelike (EQN) principal norm...

In this paper, we obtain some characterizations for a Frenet curve with the help of an alternative frame different from frame. Also, in present study consider weak biharmonic and harmonic 1-type curves by using mean curvature vector field curve. We also whose is kernel Laplacian. give theorems them Euclidean 3-space. Moreover, classifications these type curves.

v. dannon showed that spherical curves in e4 can be given by frenet-like equations, and he thengave an integral characterization for spherical curves in e4 . in this paper, lorentzian spherical timelike andspacelike curves in the space time 41 r are shown to be given by frenet-like equations of timelike andspacelike curves in the euclidean space e3 and the minkowski 3-space 31 r . thus, finding...

An orthonormal frame (f1, f2, f3) is rotation–minimizing with respect to fi if its angular velocity ω satisfies ω · fi ≡ 0 — or, equivalently, the derivatives of fj and fk are both parallel to fi. The Frenet frame (t,p,b) along a space curve is rotation–minimizing with respect to the principal normal p, and in recent years adapted frames that are rotation–minimizing with respect to the tangent ...

In this paper we deal with one of the homogeneous 3geometries, the Sol geometry. The Frenet frame and the curvature and torsion of a curve has been determined, moreover, we have computed the parametric form of geodesics, their curvatures and torsions in Theorem 4.1.

We consider a unit speed curve α in Euclidean n-dimensional space E n and denote the Frenet frame by {V 1 ,. .. , V n }. We say that α is a cylindrical helix if its tangent vector V 1 makes a constant angle with a fixed direction U. In this work we give different characterizations of such curves in terms of their curvatures.

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