Symplectic invariants for curves and integrable systems in similarity symplectic geometry

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• 作者：YanYan Li ; ChangZheng Qu
• 关键词：similarity symplectic geometry ; integrable system ; symplectic invariant ; moving frame method ; matrix Burgers equation ; 37K10 ; 37K25 ; 53A55
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：58
• 期：7
• 页码：1415-1432
• 全文大小：268 KB
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• 作者单位：YanYan Li (1)
  ChangZheng Qu (2)
  
  1. College of Mathematics and Information Science, Xianyang Normal University, Xianyang, 712000, China
  2. Department of Mathematics, Ningbo University, Ningbo, 315211, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

In this paper, similarity symplectic geometry for curves is proposed and studied. Explicit expressions of the symplectic invariants, Frenet frame and Frenet formulae for curves in similarity symplectic geometry are obtained by using the equivariant moving frame method. The relationships between the Euclidean symplectic invariants, Frenet frame, Frenet formulae and the similarity symplectic invariants, Frenet frame, Frenet formulae for curves are established. Invariant curve flows in four-dimensional similarity symplectic geometry are also studied. It is shown that certain intrinsic invariant curve flows in four-dimensional similarity symplectic geometry are related to the integrable Burgers and matrix Burgers equations.