Lightcone framed curves in the Lorentz-Minkowski 3-space
Liang Chen, Masatomo Takahashi
Abstract
For a nonlightlike nondegenerate regular curve, we have the arc-length parameter and the Frenet-Serret type formula by using a moving frame like a regular space curve in the Euclidean space. If a point of the curve moves between spacelike and timelike regions, then there is a lightlike point. In this paper, we consider mixed types of not only regular curves but also curves with singular points. In order to consider mixed type of curves with singular points, we introduce a frame, so-called the lightcone frame, and lightcone framed curves. We investigate differential geometric properties of lightcone framed curves.
Topics & Concepts
Minkowski spaceMathematicsLorentz transformationLorentz spaceSpace (punctuation)Mathematical analysisHyperboloid modelGeometryMathematical physicsPure mathematicsClassical mechanicsPhysicsComputer scienceOperating systemAdvanced Numerical Analysis TechniquesGeometric Analysis and Curvature FlowsAdvanced Differential Geometry Research