Gauss-Bonnet for Form Curvatures

Oliver Knill

Gauss-Bonnet for Form Curvatures

Combinatorics 2024-09-04 v1

Authors: Oliver Knill

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.

Keywords

differential geometry deformation theory curves

Cite

@article{arxiv.2409.01425,
  title  = {Gauss-Bonnet for Form Curvatures},
  author = {Oliver Knill},
  journal= {arXiv preprint arXiv:2409.01425},
  year   = {2024}
}