Some Characterizations of Null, Pseudo Null and Partially Null Rectifying Curves in Minkowski Space-Time

Singularity analysis of pseudo null hypersurfaces and pseudo hyperbolic hypersurfaces

“…When γ(s) be a pseudo null curve on de Sitter 3-space with the curvature κ(s) = 0, by the same methods in [6], we know the curve γ(s) is a plane curve, and γ(s) has only one order contact with hyperbolic 3-space. …”

“…In particular, when the Frenet frame along a spacelike or a timelike curve contains a null vectors, such curve is said to be a pseudo null curve. The Frenet equations of a pseudo null curve, lying fully in R 4 1 , are given in [6,11]. However, most of papers and books are studying the geometrical properties of spacelike curves without any null Fernet frames in Minkowski 4-space.…”

Osculating curves in 4-dimensional semi-Euclidean space with index 2

“…It is shown in [1] that there exists a simple relationship between the rectifying curves and centrodes, which play some important roles in mechanics and kinematics. Some characterizations of rectifying curves in Minkowski space-time are given in [6]. It is well-known that the position vector of a curve in E 3 always lies in its osculating plane B ?…”

Rectifying Curves in the Three-Dimensional Hyperbolic Space

“…Since the paper by Chen, many authors have extended the notion of rectifying curve to other ambient spaces P. Lucas and J. A. Ortega-Yagües MJOM (of dimension n ≥ 3), endowed with a Riemannian or pseudo-Riemannian metric (see, e.g., [4][5][6][7][8][9][10]14]). In all cases, the tangent vector spaces can be identified with the manifold, and this identification turns out to be crucial to make a study analogous to that made by Chen. To extend this concept to other ambient spaces, it is necessary, however, to distinguish between the manifold and its tangent vector spaces.…”