Generalized Helices on a Lightlike Cone in 3-Dimensional Lorentz-Minkowski Space

Abstract

In this paper we provide characterizations and give some properties of generalized helices in 3-dimensional Lorentz-Minkowski space that lie on a lightlike cone. Furthermore, by analyzing their projections, which turn out to be Euclidean or Lorentzian logarithmic spiral, we present their parametrizations. In particular, we also analyze planar generalized helices, that is planar intersections of a lightlike cone.

Curves in Lightlike Planes in Three-Dimensional Lorentz–Minkowski Space

“…We are further interested in the class of spherical pseudo-null curves. These results can also be found in [14][15][16] and in [17] in the case of lightlike cones. In Lorentz-Minkowski space M 3 , the following sets are considered as spheres:…”

Krivulje u 3-dimenzionalnom Minkowskijevom prostoru

“…Vidi sliku 4 desno. Euklidska elipsa je takoer Minkowskijeva kružnica, što je pokazano u [11]. Promatran je presjek svjetlosnog stošca…”