Topological structure of Gauss--Bonnet--Chern theorem and -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 -mapping topological current theory, this paper shows that the Gauss--Bonnet--Chern density (the Euler--Poincaré characteristic density) can be expressed in terms of a smooth vector field and take the form of , which means that only the zeros of contribute to . 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.
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
