The focal developable and the binormal indicatrix of a nonlightlike curve in Minkowski 3-space. (English) Zbl 0978.53004

Pei, Donghe; Sano, Takashi

Tokyo J. Math. 23, No. 1, 211-225 (2000).

The paper deals with the intrinsic geometry of curves in a pseudo Euclidean 3-space (“Minkowski 3-space”, “pe-space”). Analyzing the instantaneous kinematics of the moving trihedral the authors calculate expressions for the osculating pe-circle, the (hyper)-osculating pe-sphere and the generator of the axoidal surface belonging to a not lightlike (i.e., not isotropic) curve \(c\). The paper is not based on “classical” related references [e.g., O. Giering, “Vorlesungen über höhere Geometrie” (1982; Zbl 0493.51001)]. So besides some typos there occur some less usual terms as for example “focal developable” for the surface enveloped by the pe-normal planes of curve \(c\), “binormal indicatrix” for the pe-spherical image of the binormals of \(c\), “hyperbola and concentric pseudo sphere” for a pair of conjugate pe-spheres.

Reviewer: G.Weiß (Dresden)

MSC:

53A04	Curves in Euclidean and related spaces
53B30	Local differential geometry of Lorentz metrics, indefinite metrics

Keywords:

Minkowski space; curve theory; instantaneous kinematics

Citations:

Zbl 0493.51001