Talk:Bochner's theorem (Riemannian geometry)

Not the Bochner-Yano theorem

Referring to most recent version and wikipage title "Bochner-Yano theorem".[1] Bochner proved this in 1946, it was not proved by Bochner and Yano in 1953 as indicated. This matches what is said by Bochner and Yano's very book (although they, like Bochner's original article, only seem to state the essentially equivalent version for Killing vector fields).
Moreover it is commonly recognized in the literature as being due to Bochner. In addition to the references I have added see e.g. Besse's book "Einstein manifolds" and Aubin's "Some nonlinear problems in Riemannian geometry". (I haven't added these as references since they don't discuss the proof.)
By contrast I haven't been able to find material justifying name of "Bochner-Yano theorem". From searching google and google scholar I have found a single author, perhaps inspired by wiki's attribution, who refers/referred to it as such. Gumshoe2 (talk) 19:41, 26 February 2022 (UTC)

I have moved page title from "Bochner-Yano theorem" to "Bochner's theorem (Riemannian geometry)". With the new title, it would be very good to also include Bochner's parallel theorem on positive Ricci curvature, which is even better-known. It is naturally related since the proof is almost identical. Gumshoe2 (talk) 19:44, 26 February 2022 (UTC)