Bochner's theorem (Riemannian geometry)

In mathematics, Salomon Bochner proved in 1946 that any Killing vector field of a compact Riemannian manifold with negative Ricci curvature must be zero. Consequently the isometry group of the manifold must be finite.[1][2][3]

  1. ^ Kobayashi & Nomizu 1963, Corollary VI.5.4; Petersen 2016, Corollary 8.2.3.
  2. ^ Kobayashi 1972.
  3. ^ Wu 2017.