Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes

Details Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes

2010-09-15

arxiv.org/abs/1009.3061v1

Mathematics

Differential Geometry

15 pages, 4 figures

Scientific paper

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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