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Decomposition Theory of Spin Connection and Topological Structure of Gauss-Bonnet-Chern Theorem on Manifold With Boundary

Sheng Li·Yishi Duan
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Abstract

The index theorem of Euler-Poincaré characteristic of manifold with boundary is given by making use of the general decomposition theory of spin connection. We shows the sum of the total index of a vector field $ϕ$ and half the total of the projective vector field of $ϕ$ on the boundary equals the Euler-Poincaré characteristic of the manifold. Detailed discussion on the topological structure of the Gauss-Bonnet-Chern theorem on manifold with boundary is given. The Hopf indices and Brouwer degrees label the local structure of the Euler density.

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Sheng Li, Yishi Duan. 1999-03-10. Decomposition Theory of Spin Connection and Topological Structure of Gauss-Bonnet-Chern Theorem on Manifold With Boundary. https://arxiv.org/abs/math-ph/9903020

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