中国物理B ›› 2009, Vol. 18 ›› Issue (4): 1301-1305.doi: 10.1088/1674-1056/18/4/001

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Topological structure of Gauss--Bonnet--Chern theorem and p-branes

张欣会1, 段一士1, 田苗2   

  1. (1)Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China; (2)Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China;School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
  • 收稿日期:2008-06-08 修回日期:2008-07-04 出版日期:2009-04-20 发布日期:2009-04-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10475034).

Topological structure of Gauss--Bonnet--Chern theorem and $\tilde{p}$-branes

Tian Miao(田苗)a)b)†, Zhang Xin-Hui(张欣会)a)‡, and Duan Yi-Shi(段一士)a)   

  1. a Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China; b School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
  • Received:2008-06-08 Revised:2008-07-04 Online:2009-04-20 Published:2009-04-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10475034).

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摘要： By making use of the φ-mapping topological current theory, this paper shows that the Gauss--Bonnet--Chern density (the Euler--Poincaré characteristic χ(M) density) can be expressed in terms of a smooth vector field φ and take the form of δ(φ), which means that only the zeros of φ contribute to χ(M). This is the elementary fact of the Hopf theorem. Furthermore, it presents that a new topological tensor current of \tilde {p}-branes can be derived from the Gauss--Bonnet--Chern density. Using this topological current, it obtains the generalized Nambu action for multi \tilde p-branes.

关键词: topological structure, branes

Abstract: By making use of the $\phi$-mapping topological current theory, this paper shows that the Gauss--Bonnet--Chern density (the Euler--Poincaré characteristic $\chi(M)$ density) can be expressed in terms of a smooth vector  field ${\phi}$ and take the form of $\delta(\phi)$, which means that only the zeros of $\phi$ contribute to $\chi(M)$. This is the elementary fact of the Hopf theorem. Furthermore, it presents that a new  topological tensor current of $\tilde {p}$-branes can be derived from the Gauss--Bonnet--Chern density. Using this topological current, it obtains the generalized Nambu action for multi $\tilde p$-branes. 

Key words: topological structure, branes

中图分类号:  (Strings and branes)

  • 11.25.-w
02.40.-k (Geometry, differential geometry, and topology)