Sweeping surfaces according to quasi curve and quasi focal curve in Euclidean 3-space
Year: 2026
Type: article
Abstract: In this paper, sweeping surfaces generated by quasi curves and quasi focal curves are introduced using a quasi frame in the Euclidean 3-space. First, the singular points, the Gaussian and mean curvatures of sweeping surfaces with a quasi curve are obtained. The necessary and sufficient conditions for these surfaces to be developable, minimal, and of Weingarten type are given. Secondly, the conditions for parameter curves on these surfaces to be asymptotics, geodesics, and lines of curvature are examined. The subsequent section discusses the properties of sweeping surfaces with a quasi focal curve as the spine curve. The singular points, the Gaussian and mean curvatures of these surfaces are obtained, and the conditions for them to be developable, minimal, and of Weingarten type are given. Additionally, characterizations of parameter curves on these surfaces as asymptotics, geodesics, and lines of curvature are investigated. Several examples and visual representations are presented to support the findings. Finally, the study is enriched by incorporating comparative analyses and visual representations to demonstrate the suitability and applicability of the quasi frame for swept surfaces.
Source: Open Mathematics
Institutions: Afyon Kocatepe University, Ordu University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W7213635807