Nonnegative curvature on piecewise constant curvature spaces

Peszek, Robert

doi:10.1090/S0002-9947-1992-1059712-1

Nonnegative curvature on piecewise constant curvature spaces
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Trans. Amer. Math. Soc. 334 (1992), 303-315 Request permission

Abstract:

We consider piecewise flat and piecewise spherical spaces. We prove that every piecewise flat cobordism which is a product near the boundary and has nonnegative curvature must be trivial in the metric sense. We also obtain several restrictions for piecewise $p$-spherical manifolds with nonnegative curvature and diameter equal to $\pi p$. We prove that such a manifold must be homeomorphic to a sphere and that it is a disjoint union of minimal paths connecting two points, which have length $\pi p$.

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