## A new flow on starlike curves in $\mathbb {R}^3$

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- by Rongpei Huang and David A. Singer PDF
- Proc. Amer. Math. Soc.
**130**(2002), 2725-2735 Request permission

## Abstract:

In this note we find a new evolution equation for starlike curves in $\mathbb {R}^3$. We study the evolution of the subaffine curvature and subaffine torsion under the flow and show that it is completely integrable. The solutions to the evolution which move without changing affine shape are subaffine elastic curves. We integrate the subaffine elastica by quadratures.## References

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## Additional Information

**Rongpei Huang**- Affiliation: Department of Mathematics, East China Normal University, Shanghai, 200062, People’s Republic of China
- Email: rphuang@math.ecnu.edu.cn
**David A. Singer**- Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106-7058
- Email: das5@po.cwru.edu
- Received by editor(s): February 4, 2000
- Published electronically: April 11, 2002
- Communicated by: Wolfgang Ziller
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**130**(2002), 2725-2735 - MSC (2000): Primary 53A04; Secondary 53A15
- DOI: https://doi.org/10.1090/S0002-9939-02-06631-5
- MathSciNet review: 1900890