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edit approved Jun 18, 2018 at 20:23

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Riemannian metric on the sphere with at least one negative sectional curvature at every point

Does there exist a Riemannian metric on the $n$-sphere ($n > 2$) such that at each point some (but not every) sectional curvature is negative?

For $n=2$ it is easily seen that such a metric cannot exist.

dg.differential-geometry riemannian-geometry negative-curvature

asked Jun 18, 2018 at 19:47

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