Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space

Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space

In the present paper, we defined the circular evolutes and involutes for a given spacelike framed curve with respect to Bishop directions in Minkowski 3-space. Then, we studied the essential duality relations among parallel curves, normal surfaces, and circular evolutes and involutes. Furthermore, w...

Full description

Saved in:
Bibliographic Details
Published in:AIMS mathematics Vol. 9; no. 3; pp. 5688 - 5707
Main Authors: Zhang, Wei, Li, Pengcheng, Pei, Donghe
Format: Journal Article
Language:English
Published: AIMS Press 01-01-2024
Subjects:
circular evolutes
involutes
normal surfaces
parallel curves
spacelike framed curves
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In the present paper, we defined the circular evolutes and involutes for a given spacelike framed curve with respect to Bishop directions in Minkowski 3-space. Then, we studied the essential duality relations among parallel curves, normal surfaces, and circular evolutes and involutes. Furthermore, we also studied the duality relations of their singularities. Based on these studies, we found that it is crucially important to consider the duality relations among different geometric objects for the research of submanifolds with singularities.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024276