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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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 $ 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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Article copyright: © Copyright 1992 American Mathematical Society