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Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes

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 نشر من قبل Andrea Young
 تاريخ النشر 2010
  مجال البحث
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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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