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arXiv · 1509.05003

Elementary Proofs Of The Gauss-Bonnet Theorem And Other Integral Formulas In $\Bbb R^3$

Daniel Mayost
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Abstract

For a compact differentiable surface with boundary embedded in $\Bbb R^3$, we give simple proofs of the Gauss-Bonnet theorem, Poincar\'{e}-Hopf theorem, and several other integral formulas. We complete all of the proofs without using fundamental or differential forms.

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Daniel Mayost. 2015-09-16. Elementary Proofs Of The Gauss-Bonnet Theorem And Other Integral Formulas In $\Bbb R^3$. https://arxiv.org/abs/1509.05003

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