%0 Journal Article
%T Eigenvalue estimates for a class of elliptic differential operators on compact manifolds
%A Hil¨¢rio Alencar
%A Greg¨®rio Silva Neto
%A Detang Zhou
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1304.5268v2