Commun. Korean Math. Soc. 2019; 34(1): 333-349
Online first article November 5, 2018 Printed January 31, 2019
https://doi.org/10.4134/CKMS.c180087
Copyright © The Korean Mathematical Society.
Rashad A. Abdel-Baky
University of Assiut
The paper study the curvature theory of a line-trajectory of constant Disteli-axis, according to the invariants of the axodes of moving body in spatial motion. A necessary and sufficient condition for a line-trajectory to be a constant Disteli-axis is derived. From which new proofs of the Disteli's formulae and concise explicit expressions of the inflection line congruence are directly obtained. The obtained explicit equations degenerate into a quadratic form, which can easily give a clear insight into the geometric properties of a line-trajectory of constant Disteli-axis with the theory of line congruence. The degenerated cases of the Burmester lines are discussed according to dual points having specific trajectories.
Keywords: E. Study's map, axodes, line congruence, Disteli's formula
MSC numbers: 53A04, 53A05, 53A17
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