Haibo Yu
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Haibo Yu has a total of 1 co-authors. Here are the top co-authors by number of shared publications:
- Liang Chen
School of Mathematics and Statistics, Northeast Normal University, Changchun, People’s Republic of China
2 shared publications
Latest Publications
- 26 September 2025
- Published by Springer Nature in Mediterranean Journal of Mathematics
- Vol. 22 (7) , 1-34
Focal Surfaces and Evolutes of Framed Curves in Hyperbolic 3-Space from the Viewpoint of Legendrian Duality
- 26 September 2025
- Published by Springer Nature in Mediterranean Journal of Mathematics
- Vol. 22 (7) , 1-34
Focal Surfaces and Evolutes of Framed Curves in Hyperbolic 3-Space from the Viewpoint of Legendrian Duality
- Open Access
Focal surfaces and evolutes of framed curves in hyperbolic 3-space from the viewpoint of Legendrian duality
A hyperbolic framed curve is a smooth curve with a moving frame in hyperbolic 3-space. It may have singularities. By using this moving frame, we can investigate the differential geometry properties of curves, even at singular points. In fact, we consider the focal surfaces and evolutes of hyperbolic framed curves by using Legendrian dualities which developed by Chen and Izumiya. The focal surfaces are the dual surfaces of tangent indicatrix of original curves. Moreover, classifications of singularities of the serval dual surfaces are shown. By this, we give the relationship among focal surfaces, evolutes and dual surfaces of evolutes. Finally, we study duality relations of singularities between focal surfaces and dual surfaces of evolutes.
Open AccessFocal surfaces and evolutes of framed curves in hyperbolic 3-space from the viewpoint of Legendrian duality
A hyperbolic framed curve is a smooth curve with a moving frame in hyperbolic 3-space. It may have singularities. By using this moving frame, we can investigate the differential geometry properties of curves, even at singular points. In fact, we consider the focal surfaces and evolutes of hyperbolic framed curves by using Legendrian dualities which developed by Chen and Izumiya. The focal surfaces are the dual surfaces of tangent indicatrix of original curves. Moreover, classifications of singularities of the serval dual surfaces are shown. By this, we give the relationship among focal surfaces, evolutes and dual surfaces of evolutes. Finally, we study duality relations of singularities between focal surfaces and dual surfaces of evolutes.