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arXiv · 1009.3061

Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes

Daniel Champion·Andrew Marchese·Jacob Miller·Andrea Young
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Abstract

In [7], a notion of constant scalar curvature metrics on piecewise flat manifolds is defined. Such metrics are candidates for canonical metrics on discrete manifolds. In this paper, we define a class of vertex transitive metrics on certain triangulations of $\mathbb{S}^3$; namely, the boundary complexes of cyclic polytopes. We use combinatorial properties of cyclic polytopes to show that, for any number of vertices, these metrics have constant scalar curvature.

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Daniel Champion, Andrew Marchese, Jacob Miller, Andrea Young. 2010-09-15. Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes. https://arxiv.org/abs/1009.3061

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