regular curve


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regular curve

[′reg·yə·lər ′kərv]
(mathematics)
A curve that has no singular points.
References in periodicals archive ?
Murata Umehara [9] gave a representation formula for complete flat fronts with non-empty singular set, and proved the four vertex type theorem: Let [xi] : [S.sup.1] [right arrow] [S.sup.2] be a regular curve without inflection points, and [alpha] = a(t)dt a 1-form on [S.sup.1] = R/2[pi]Z such that [mathematical expression not reproducible] holds.
We can express a new frame different from the Frenet frame for a regular curve. Let [alpha]: I [subset] R [right arrow] [S.sup.2.sub.1] be a regular unit speed curve lying fully on [S.sup.2.sub.1].
If the position vector of a regular curve a is composed by the Frenet frame vectors of another regular curve [beta], then the curve a is called a Smarandache curve [2].
In the theory of curves in Euclidean space, one of the important and interesting problems is the characterization of a regular curve. In the solution of the problem, the curvature [kappa] and the torsion [tau] of a regular curve have an effective role.
Recall that if a regular curve has constant Frenet-Serret curvature ratios (i.e., [tau]/k and [sigma]/[tau] are constants), it is called a ccr-curve [4,5].
12 This line is a regular curve in the general plans, and only takes this more complex form in the larger scale stage plan.
Let [alpha](s), s being the arclength parameter, be a non-null regular curve in semi-Euclidean space [E.sup.2n+1.sub.v].