Singular Surfaces of Osculating Circles in Three-Dimensional Euclidean Space

Kemeng Liu, Zewen Li and Donghe Pei ()
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Kemeng Liu: School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
Zewen Li: School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
Donghe Pei: School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Mathematics, 2023, vol. 11, issue 17, 1-12

Abstract: In this paper, we study the surfaces of osculating circles, which are the sets of all osculating circles at all points of regular curves. Since the surfaces of osculating circles may be singular, it is necessary to investigate the singular points of these surfaces. However, traditional methods and tools for analyzing singular properties have certain limitations. To solve this problem, we define the framed surfaces of osculating circles in the Euclidean 3-space. Then, we discuss the types of singular points using the theory of framed surfaces and show that generic singular points of the surfaces consist of cuspidal edges and cuspidal cross-caps.

Keywords: surfaces of osculating circles; framed surfaces; singularities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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