Lawson-Yau theorem
Statement
If a compact connected manifold is equipped with an effective action of a compact Lie group whose identity component is non-Abelian, it admits a Riemannian metric of positive scalar curvature which is invariant under the group action.
References
- Scalar curvature, non-Abelian group actions, and the degree of symmetry of exotic spheres by H. Blaine Lawson, Jr., and S.T. Yau, Comment. Math. Helv. 49 (1974), 232-244
- Positive scalar curvature with symmetry by Bernhard Yanke