Symplectic invariants for curves and integrable systems in similarity symplectic geometry  

作　　者：LI YanYan QU ChangZheng 

机构地区：[1]College of Mathematics and Information Science, Xianyang Normal University [2]Department of Mathematics, Ningbo University

出　　处：《Science China Mathematics》2015年第7期1415-1432,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11471174 and 11101332);Natural Science Foundation of Shaanxi Province(Grant No.2014JM-1002);the Natural Science Foundation of Xianyang Normal University of Shaanxi Province(Grant No.14XSYK004)

摘　　要：In this paper, similarity symplectic geometry for curves is proposed and studied. Explicit expressions of the symplectic invariants, Frenet frame and Prenet 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.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.

关 键 词：similarity symplectic geometry integrable system symplectic invariant moving frame method matrix Burgers equation 

分 类 号：O175.5[理学—数学]