Elementary Proofs Of The Gauss-Bonnet Theorem And Other Integral Formulas In \Bbb R³

2015/09/16 by Daniel Mayost, Mayost, Daniel
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.DG

paper · pdf · doi:10.48550/arxiv.1509.05003

arxiv created 2015/09/16 · openalex publication_date 2015/09/16 · arxiv updated 2015/09/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For a compact differentiable surface with boundary embedded in \Bbb R³, we give simple proofs of the Gauss-Bonnet theorem, Poincaré-Hopf theorem, and several other integral formulas. We complete all of the proofs without using fundamental or differential forms.

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