%0 Journal Article
%T The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold in dimension seven
%A Stefan Ivanov
%A Alexander Petkov
%A Dimiter Vassilev
%J Mathematics
%D 2012
%I arXiv
%X A version of Lichnerowicz' theorem giving a lower bound of the eigenvalues of the sub-Laplacian under a lower bound on the Sp(1)Sp(1) component of the qc-Ricci curvature on a compact seven dimensional quaternionic contact manifold is established. It is shown that in the case of a seven dimensional compact 3-Sasakian manifold the lower bound is reached if and only if the quaternionic contact manifold is a round 3-Sasakian sphere.
%U http://arxiv.org/abs/1210.6932v1