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arXiv · 2112.03614

Surfaces of osculating circles in Euclidean space

Rafael López·Cetin Camci·Ali Ucum·Kazim Ilarslan
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Abstract

We introduce a new class of surfaces in Euclidean $3$-space, called surfaces of osculating circles, using the concept of osculating circle of a regular curve. These surfaces contain a uniparametric family of planar lines of curvature. In this paper, we classify those ones that are canal surfaces and Weingarten surfaces.

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Rafael López, Cetin Camci, Ali Ucum, Kazim Ilarslan. 2021-12-07. Surfaces of osculating circles in Euclidean space. https://arxiv.org/abs/2112.03614

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