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单词 SphereTheoremFromGlobalDifferentialGeometry
释义

sphere theorem from global differential geometry


This theorem, as do Carmo refers it, is one of the most beautiful theorems in Riemannian geometry:

sphere theorem. Let M be a n-dimensional compact simply connected Riemannian manifoldMathworldPlanetmath, whose sectional curvatureMathworldPlanetmath K satisfies

0<Kmax/4<KKmax

Then M is homeomorphic to a sphere.

References

  • 1 M. P. do Carmo, Riemannian Geometry, Birkhäuser, Boston, 1992.
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