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Mathematische Zeitschrift

, Volume 290, Issue 1–2, pp 167–193 | Cite as

Vortex filament on symmetric Lie algebras and generalized bi-Schrödinger flows

  • Qing DingEmail author
  • Youde Wang
Article

Abstract

In this article, we display an evolving model on symmetric Lie algebras from a purely geometric way by using the Hamiltonian (or para-Hamiltonian) gradient flow of a fourth order functional called generalized bi-Schrödinger flows, which corresponds to the Fukumoto–Moffatt’s model in the theory of moving curves, or the vortex filament in physical words, in \(\mathbb {R}^3\). The theory of vortex filament in \(\mathbb {R}^3\) or \(\mathbb {R}^{2,1}\) up to the third-order approximation is shown to be generalized to symmetric Lie algebras in a unified way.

Keywords

Moving curve Bi-Schrödinger flow Lie algebra Para-Kähler structure 

Notes

Acknowledgements

The authors would thank the referee for his/her helpful comments and suggestions. The authors are supported by the National Natural Science Foundation of China (Grant Nos.10971030, 11531012 and 11471316) and the foundation of Shanghai Educational Committee (No. 14ZZ002).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China
  2. 2.College of Mathematics and Information SciencesGuangzhou UniversityGuangzhouPeople’s Republic of China
  3. 3.Academy of Mathematics and Systematic SciencesChinese Academy SciencesBeijingPeople’s Republic of China

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