Suppose I have a Riemann surface, $M$ which admits a metric of negative Guassian curvature.
Is it known if the deleted product:
$M\times M\backslash \{ (m,m) : m\in M\}$ admits a (complete) metric of negative sectional curvature or not?
Suppose I have a Riemann surface, $M$ which admits a metric of negative Guassian curvature.
Is it known if the deleted product:
$M\times M\backslash \{ (m,m) : m\in M\}$ admits a (complete) metric of negative sectional curvature or not?
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