Nonnegative Curvature on Piecewise Constant Curvature Spaces
Copyright policy )Nonnegative Curvature on Piecewise Constant Curvature Spaces
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 p -spherical manifolds with nonnegative curvature and diameter equal to π p \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 π p \pi p .
- University of Maryland, Baltimore United States
piecewise flat cobordism, Triangulating manifolds, piecewise flat manifolds, Cobordism in PL-topology, nonnegative curvature, piecewise spherical spaces, Geodesics in global differential geometry, Global Riemannian geometry, including pinching
piecewise flat cobordism, Triangulating manifolds, piecewise flat manifolds, Cobordism in PL-topology, nonnegative curvature, piecewise spherical spaces, Geodesics in global differential geometry, Global Riemannian geometry, including pinching
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