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

1999/03/10 by Sheng Li, Li, Sheng, Yi-Shi Duan +2
Computer Science · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Topological and Geometric Data Analysis #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/9903020

Revtex, 13 pages, no figure

arxiv created 1999/03/10 · openalex publication_date 1999/03/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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