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Inner structure of Gauss-Bonnet-Chern Theorem and the Morse theory

Yi-shi Duan·Peng-ming Zhang
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Abstract

We define a new one form H^A based on the second fundamental tensor H^abA, the Gauss-Bonnet-Chern form can be novelly expressed with this one-form. Using the phi-mapping theory we find that the Gauss-Bonnet-Chern density can be expressed in terms of the delta-function and the relationship between the Gauss-Bonnet-Chern theorem and Hopf-Poincare theorem is given straightforwardly. The topological current of the Gauss-Bonnet-Chern theorem and its topological structure are discussed in details. At last, the Morse theory formula of the Euler characteristic is generalized.

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Yi-shi Duan, Peng-ming Zhang. 2002-12-19. Inner structure of Gauss-Bonnet-Chern Theorem and the Morse theory. https://doi.org/10.1142/s0217732301006004

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