Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0978.53004
Pei, Donghe; Sano, Takashi
The focal developable and the binormal indicatrix of a nonlightlike curve in Minkowski 3-space. (English)
[J] Tokyo J. Math. 23, No.1, 211-225 (2000). ISSN 0387-3870

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., {\it 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.
[G.Weiss (Dresden)]

MSC 2000:: *53A04 Curves in Euclidean space
53B30 Lorentz metrics, indefinite metrics

Keywords: Minkowski space; curve theory; instantaneous kinematics

Citations: Zbl 0493.51001

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]