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H. Kocayigit, N. Yaz, C. Camci, H. H. Hacisalihoglu

On the explicit characterization of spherical curves in n-dimensional Euclidean space

It is known that a curve in 3-dimensional Euclidean space is spherical if and only if

where k₁ and k₂ are its first curvature function and second curvature function, respectively. In 1971, integral form of (1) was given [2] as

In the present work, a) it is given another method for (2); b) it is shown that the differential equation characterizing a spherical curve in n-dimensional Euclidean space n ≥ 3 can be solved explicitly to express nth curvature function of the curve in terms of its curvatures and its other curvature functions; c) it is shown that integral form of the generalization of (1) gives us (2) as a spherical case for n = 3.

Journal of Inverse and Ill-posed Problems, Walter de Gruyter

Print ISSN: 0928-0219
Volume: 11, 09/2003
Pages: 245 - 254

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