Talk:Smooth Manifold admits Riemannian Metric

Meaning of "admits"
I agree that "admits" for a firstcomer sounds vague. At the same time there are plenty of source showing this exact formulation of the theorem. Improvement is needed, but I worry that this may require reading several proofs (which are not present in my books) and then finding the common denominator. Already my comment about sufficient structure provided by smooth manifolds was an observation of types of proofs, not a copy of any text.--Julius (talk) 23:35, 9 November 2022 (UTC)


 * Is the "admits" not defined in your book? Then I think we need to take the definition from another source. It is really vague. To understand the theorem, I first need to think about what it should be. Does it means that there exists some diffeomorphism between the given smooth manifold and some Riemann manifold? I am not sure how I can formulate this theorem correctly. --Usagiop (talk) 00:30, 10 November 2022 (UTC)


 * Vaguely, however, I know what you mean. --Usagiop (talk) 00:40, 10 November 2022 (UTC)