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user 3948
6
votes
Accepted
The midpoint geodesic
The answer is no.
Define the manifold
Let $f$ be a smooth function on $\mathbb{R}$ satisfying
$f(r) = |r|$ for $|r| > 3$
$f(r) > 0$
$f''(r) \geq 0$.
The corresponding warped product metric on …
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