4
$\begingroup$

Let $M$ be a compact smooth manifold and $g$ a Riemannian metric on $M$.

By the solution of the Yamabe problem, there exists a metric $\tilde{g}$ of constant scalar curvature on $M$ which is conformal to $g$.

Suppose $g$ has positive Ricci curvature. Does there exist a metric $\tilde{g}$ conformal to $g$ such that $\tilde{g}$ has constant scalar curvature and positive Ricci curvature as well?

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.