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arXiv · 2409.01425

Gauss-Bonnet for Form Curvatures

Oliver Knill
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Abstract

We look at curvatures that are supported on k-dimensional parts of a simplicial complex G. These curvature all satisfy the Gauss-Bonnet theorem, provided that the k-dimensional simplices cover $G$. Each of these curvatures can be written as an expectation of Poincare-Hopf indices. Linear or non-linear wave dynamics with discrete or continuous time allow to deform these curvatures while keeping the Gauss-Bonnet property.

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Oliver Knill. 2024-09-02. Gauss-Bonnet for Form Curvatures. https://arxiv.org/abs/2409.01425

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