Higher order Dirac structure and Nambu-Poisson geometry  

作　　者：Yanhui BI Jia LI 

机构地区：[1]Center for Mathematical Sciences,College of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China

出　　处：《Frontiers of Mathematics in China》2024年第1期37-56,共20页中国高等学校学术文摘·数学（英文）

摘　　要：This paper studies the properties of Nambu-Poisson geometry from the(n-l,k)-Dirac structure on a smooth manifold M.Firstly,we examine the automorphism group and infinitesimal on higher order Courant algebroid,to prove the integrability of infinitesimal Courant automorphism.Under the transversal smooth morphismΦ:N-→M and anchor mapping of M on(n-1,k)-Dirac structure,it's holds that the pullback(n-1,k)-Dirac structure on M turns out an(n-1,k)-Dirac structure on N.Then,given that the graph of Nambu-Poisson structure takes the form of(n-1,n-2)-Dirac structure,it follows that the single parameter variety of Nambu-Poisson structure is related to one variety closed n-symplectic form under gauge transformation.WhenΦ:N-→M is taken as the immersion mapping of(n-1)-cosymplectic submanifold,the pullback Nambu-Poisson structure on M turns out the Nambu-Poisson structure on N.Finally,we discuss the(n-1,O)-Dirac structure on M can be integrated into a problem of(n-1)-presymplectic groupoid.Under the mapping II:M-→M/H,the corresponding(n-1,O)-Dirac structure is F and E respectively.If E can be integrated into(n-1)-presymplectic groupoid(g,2),then there exists the only,such that the corresponding integral of F is(n-1)-presymplectic groupoid(g,).

关 键 词：Nambu-Poisson structure n-symplectic structure (n-1 k)-Dirac structure INTEGRABILITY 

分 类 号：O18[理学—数学]