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)
a Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China; b School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
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.
Received: 08 June 2008
Revised: 04 July 2008
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of
China (Grant No 10475034).
Cite this article:
Tian Miao(田苗), Zhang Xin-Hui(张欣会), and Duan Yi-Shi(段一士) Topological structure of Gauss--Bonnet--Chern theorem and $\tilde{p}$-branes 2009 Chin. Phys. B 18 1301
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