Let $(M,g)$ be a Riemannian manifold; for the sake of simplicity we assume that its group of isometries is trivial. If we consider the same manifold equipped with another metric $g'$, what is the asymptotic of the Gromov–Hausdorff distance between $(M,g)$ and $(M,g')$ as $g'\to g$? (I feel embarrassed asking such a basic question, but I had no luck finding this formula in the literature.)
$\begingroup$
$\endgroup$
Add a comment
|