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The Almost Schur Lemma in Quaternionic Contact Geometry
Stefan Ivanov, Alexander Petkov
We establish quaternionic contact (qc) versions of the so called Almost Schur Lemma, which give estimations of the qc scalar curvature on a compact qc manifold to be a constant in…
The CR Almost Schur Lemma and the positivity conditions
Stefan Ivanov, Alexander Petkov
We establish a new version of the CR almost Schur Lemma which gives an estimation of the pseudohermitian scalar curvature on a compact strictly pseudoconvex pseudohermitian manifol…
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…
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…
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…