3 papers
math.DG2013
The Obata sphere theorems on a quaternionic contact manifold of dimension bigger than seven
Stefan Ivanov, Alexander Petkov, Dimiter Vassilev
We prove a quaternionic contact versions of the Obata's sphere theorems. We show that if the first positive eigenvalue of the sub-Laplacian on a compact qc manifold of dimension bi…
math.DG2012
The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold in dimension seven
Stefan Ivanov, Alexander Petkov, Dimiter Vassilev
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 compa…
math.DG2010
HKT manifolds with holonomy SL(n,H)
Stefan Ivanov, Alexander Petkov
We show that on an HKT manifold the holonomy of the Obata connection is contained in SL(n,H) if and only if the Lee form is an exact one form. As an application, we show compact HK…