Isometry groups of Riemannian manifolds with bounded norms
A classical theorem of \textit{S.~Bochner} implies that the isometry group of a compact Riemannian manifold with negative Ricci curvature is finite. In [Duke Math. J. 76, No. 1, 59--73 (1994; Zbl 0820.53045)] \textit{X.~Dai, Z. Shen} and \textit{G.~Wei} improved this by showing that there is a bound depending on geometric data and on the order of the isometry group of a compact manifold with negative Ricci curvature. In this paper the author generalizes these results using integral bounds on Ricci curvature and the concept of norm of a Riemannian manifold introduced by \textit{P. Petersen} [Riemannian geometry. 2nd ed. Graduate Texts in Mathematics 171, Springer, (New York) (2006; Zbl 1220.53002)].
scientific article; zbMATH DE number 5076982
scientific article