| Topological structure of Gauss-Bonnet-Chern theorem and -branes |
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| 引用本文： | 田苗,张欣会,段一士.Topological structure of Gauss-Bonnet-Chern theorem and -branes[J].中国物理 B,2009,18(4):1301-1305. |
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| 作者姓名： | 田苗 张欣会 段一士 |
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| 作者单位： | Institute of Theoretical Physics, Lanzhou
University,
Lanzhou 730000, China;School of Mathematics, Physics and Software Engineering,
Lanzhou Jiaotong University, Lanzhou 730070, China;Institute of Theoretical Physics, Lanzhou
University,
Lanzhou 730000, China;Institute of Theoretical Physics, Lanzhou
University,
Lanzhou 730000, China |
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| 基金项目： | 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 -branes can be derived from the Gauss-Bonnet-Chern density. Using this topological current, it obtains the generalized Nambu action for multi -branes.
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| 关 键 词： | topological structure branes |
| 收稿时间： | 6/8/2008 12:00:00 AM |
| 修稿时间： | 7/4/2008 12:00:00 AM |
Topological structure of Gauss--Bonnet--Chern theorem and p-branes |
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| Tian Miao,Zhang Xin-Hui and Duan Yi-Shi.Topological structure of Gauss--Bonnet--Chern theorem and p-branes[J].Chinese Physics B,2009,18(4):1301-1305. |
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| Authors: | Tian Miao Zhang Xin-Hui and Duan Yi-Shi |
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| Institution: | Institute of Theoretical Physics, Lanzhou
University,
Lanzhou 730000, China; Institute of Theoretical Physics, Lanzhou
University,
Lanzhou 730000, China;School of Mathematics, Physics and Software Engineering,
Lanzhou Jiaotong University, Lanzhou 730070, China |
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| Abstract: | By making use of the $\phi$-mapping topological current theory, this
paper shows that the Gauss--Bonnet--Chern density (the
Euler--Poincar\'{e} characteristic $\chi(M)$ density) can be
expressed in terms of a smooth vector field ${\bm \phi}$ and take
the form of $\delta(\bm \phi)$, which means that only the zeros of
$\bm \phi$ 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. |
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| Keywords: | topological structure branes |
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