Characterizations of Spacelike Slant Helices In Minkowski 3-Space

In this paper, we investigate tangent indicatrix, principal normal indicatrix and binormal indicatrix of a spacelike curve with spacelike, timelike and null principal normal vector in Minkowski 3-space E3 1 and we construct their Frenet equations and curvature functions. Moreover, we obtain some differential equations which characterize for a spacelike curve to be a slant helix by using the Frenet apparatus of spherical indicatrix of the curve. Also related examples and their illustrations are given. Mathematics Subject Classification 2010: 53A04, 53C50.

Characterization of Speherical Helices in Euclidean 3-Space

In this paper, we calculate Frenet frames of the tangent indicatrix (t), principal normal indicatrix (n) and binormal indicatrix (b) of the curve α in ℝ3 which are spherical curves. Also, we give some differential equations which are characterizations for (t), (n) and (b) to be general helix. Morever we give a characterization for tangent indicatrix (t) to be a circle.

Singularities of Focal Surfaces of Null Cartan Curves in Minkowski 3-Space

Singularities of the focal surfaces and the binormal indicatrix associated with a null Cartan curve will be investigated in Minkowski 3-space. The relationships will be revealed between singularities of the above two subjects and differential geometric invariants of null Cartan curves; these invariants are deeply related to the order of contact of null Cartan curves with tangential planar bundle of lightcone. Finally, we give an example to illustrate our findings.