Characterization of dual curves using the theory of infinitesimal bending

Mathematical Methods in the Applied Sciences, Journal Year: 2024, Volume and Issue: 47(11), P. 8626 - 8637

Published: March 12, 2024

In this paper, we generalize the main ideas and statements of theory infinitesimal bending in Euclidean 3‐space to dual curves . The basic condition introduce is invariance arc length with appropriate precision. Necessary sufficient conditions for field be an are given. Some useful formulas facts about obtained. An explicit characterization spherical curve presented, corresponding decomposed into vectors Frenet frame. Finally, some examples given illustrate our results.

Language: Английский

Generalized null Cartan helices and principal normal worldsheets in Minkowski 3-space

Modern Physics Letters A, Journal Year: 2024, Volume and Issue: 39(10)

Published: March 28, 2024

We give a method for constructing generalized null Cartan helices, which may have singularities, by using regular space-like plane curves and smooth functions in Minkowski 3-space. also study the principle normal worldsheet, is deeply related to helices from viewpoint of singularity theory.

Language: Английский