New Bochner type theorems

A classical theorem of Bochner asserts that the isometry group of a compact Riemannian manifold with negative Ricci curvature is finite. In this paper we give several extensions of Bochner's theorem by allowing small positive Ricci curvature.

Automated summary

Bochner's classical theorem states that the isometry group of a compact Riemannian manifold with negative Ricci curvature is finite. In this paper, we provide several extensions of Bochner's theorem by allowing small positive Ricci curvature.