The Obata sphere theorems on a quaternionic contact manifold of dimension bigger than seven
نویسندگان
چکیده
منابع مشابه
The Obata Sphere Theorems on a Quaternionic Contact Manifold of Dimension Bigger than Seven
On a compact quaternionic contact (qc) manifold of dimension bigger than seven and satisfying a Lichnerowicz type lower bound estimate we show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value then, up to a homothety of the qc structure, the manifold is qc equivalent to the standard 3-Sasakian sphere. The same conclusion is shown to hold on a non-compa...
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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 man...
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The conformal infinity of a quaternionic-Kähler metric on a 4n-manifold with boundary is a codimension 3-distribution on the boundary called quaternionic contact. In dimensions 4n− 1 greater than 7, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7, we prove a criterion for quaternionic contact structures to be the...
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ژورنال
عنوان ژورنال: Journal of Spectral Theory
سال: 2017
ISSN: 1664-039X
DOI: 10.4171/jst/187