Eigenvalue estimates for a class of elliptic differential operators on compact manifolds

Abstract

The motivation of this paper is to study a second order elliptic operator which appears naturally in Riemannian geometry, for instance in the study of hypersurfaces with constant $r$-mean curvature. We prove a generalized Bochner-type formula for such a kind of operators and as applications we obtain some sharp estimates for the first nonzero eigenvalues in two special cases. These results can be considered as generalizations of the Lichnerowicz-Obata Theorem.

31 pages. To appear in Bulletin of the Brazilian Mathematical Society, New Series. Final version attending the suggestions of referee

References in corpus (1)

• An almost-Schur type lemma for symmetric $(2,0)$ tensors and applications

Cited by in corpus (1)

• Eigenvalue estimates for a class of elliptic differential operators in divergence form