Why if a connected manifold has all its prinvipal curvatures zero, then it must be an hyperplane?
Manifold with all principal curvatures zero.
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differential-geometry
curvature
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0You mean a connected hypersurface in $\Bbb R^{n+1}$? It must be contained in a hyperplane, yes. – 2017-01-10
1 Answers
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HINT: If all principal curvatures are $0$, show that the normal vector must be constant on the hypersurface.