The Non-compact Case
A closely related question is the so-called "non-compact Yamabe problem", which asks: on a smooth, complete Riemannian manifold (M,g) which is not compact, does there exist a conformal metric of constant scalar curvature that is also complete? The answer is no, due to counterexamples given by Jin (1988).
Read more about this topic: Yamabe Problem
Famous quotes containing the word case:
“He was then in his fifty-fourth year, when even in the case of poets reason and passion begin to discuss a peace treaty and usually conclude it not very long afterwards.”
—G.C. (Georg Christoph)
Related Phrases
Related Words