Envelopes created by sphere families in Euclidean 3-space

2025/11/03 by Nishimura, Takashi, Takahashi, Masatomo, Wang, Yongqiao
#51M15 #53A05 #57R45 #58C25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.01611

Abstract

In this paper, on envelopes created by sphere families in Euclidean 3-space, all four basic problems (existence problem, representation problem, problem on the number of envelopes, problem on relationships of definitions) are solved.

Citations

• Bertrand framed surfaces in the Euclidean 3-space and its applications
• Envelopes of straight line families in the plane
• Envelopes created by circle families in the plane
• Anti-orthotomics of frontals and their applications
• Singularities of Frontals

Related

• Envelopes created by circle families in the plane
• Envelopes created by pseudo-circle families in the Minkowski plane
• Envelopes of straight line families in the plane
• Applications of Envelopes
• On envelopes of circle families in the plane