Titlebook: General Theory of Irregular Curves; A. D. Alexandrov,Yu. G. Reshetnyak Book 1989 Kluwer Academic Publishers 1989 convergence.differentiabl

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BOGUS

BARK

Theory of a Turn for Curves on an ,-Dimensional Sphere,In the space . let us arbitrarily fix an origin .. The symbol Ω. will henceforth denote an .-dimensional sphere in the space . of radius equal to 1 and the centre ., . An arbitrary point . ∈ Ω. will be associated with the vector . ∈ . which is a radius-vector of the point . with respect to the point ..

Horizon

Osculating Planes and Class of Curves with an Osculating Plane in the Strong Sense,Let us begin by making certain remarks concerning the notion of orientation for the case of two-dimensional planes in ..

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Torsion of a Curve in a Three-Dimensional Euclidean Space,Studying a turn of a curve employing the integro-geometrical relations obtained above, required some preliminary considerations of the notion of a turn of a curve lying in one straight line. In an analogous way, studying a torsion of a spatial curve is based on considerations referring to plane curves.

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https://doi.org/10.1007/978-94-009-2591-5convergence; differentiable manifold; integral; manifold; polygon

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Monotonous

https://doi.org/10.1007/978-3-658-18708-8oints, i.e., a finite sequence of the points of ., such that . ≤ . ≤ .. Let us set .. The least upper boundary of the quantity s(.) on the set of all chains of the curve . is called a length of the curve . and is denoted as s(.). The curve . is termed rectifiable if its length is finite.

congenial

General Notion of a Curve,chet. Here we are going to dwell in detail on the definition of a curve with the aim of clarifying certain peculiarities that are important while discussing the theory of curves, and of presenting the definition of a curve in a more geometrical form as compared to the classical definition by M. Frechet.

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