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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-01-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024276?viewType=HTML |
| _version_ | 1827346276422778880 |
|---|---|
| author | Wei Zhang Pengcheng Li Donghe Pei |
| author_facet | Wei Zhang Pengcheng Li Donghe Pei |
| author_sort | Wei Zhang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-07T23:28:41Z |
| format | Article |
| id | doaj.art-6f47ff7a826147ae8728c1b3ba009fa7 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-07T23:28:41Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-6f47ff7a826147ae8728c1b3ba009fa72024-02-21T01:23:29ZengAIMS PressAIMS Mathematics2473-69882024-01-01935688570710.3934/math.2024276Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-spaceWei Zhang0Pengcheng Li1Donghe Pei 21. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China3. School of Mathematics and Statistics, Yili Normal University, Yining 835000, China2. Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, ChinaIn 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.https://www.aimspress.com/article/doi/10.3934/math.2024276?viewType=HTMLspacelike framed curvescircular evolutesinvolutesparallel curvesnormal surfaces |
| spellingShingle | Wei Zhang Pengcheng Li Donghe Pei Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space AIMS Mathematics spacelike framed curves circular evolutes involutes parallel curves normal surfaces |
| title | Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space |
| title_full | Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space |
| title_fullStr | Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space |
| title_full_unstemmed | Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space |
| title_short | Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space |
| title_sort | circular evolutes and involutes of spacelike framed curves and their duality relations in minkowski 3 space |
| topic | spacelike framed curves circular evolutes involutes parallel curves normal surfaces |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024276?viewType=HTML |
| work_keys_str_mv | AT weizhang circularevolutesandinvolutesofspacelikeframedcurvesandtheirdualityrelationsinminkowski3space AT pengchengli circularevolutesandinvolutesofspacelikeframedcurvesandtheirdualityrelationsinminkowski3space AT donghepei circularevolutesandinvolutesofspacelikeframedcurvesandtheirdualityrelationsinminkowski3space |