Nonnegative curvature on piecewise constant curvature spaces

Author:
Robert Peszek

Journal:
Trans. Amer. Math. Soc. **334** (1992), 303-315

MSC:
Primary 57Q99; Secondary 53C20

MathSciNet review:
1059712

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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 -spherical manifolds with nonnegative curvature and diameter equal to . 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 .

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DOI:
https://doi.org/10.1090/S0002-9947-1992-1059712-1

Article copyright:
© Copyright 1992
American Mathematical Society