The Sharp Lower Bound of the First Eigenvalue of the Sub-laplacian on a Quaternionic Contact Manifold in Dimension 7
نویسندگان
چکیده
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.
منابع مشابه
The Sharp Lower Bound of the First Eigenvalue of the Sub-laplacian on a Quaternionic Contact Manifold
The main technical result of the paper is a Bochner type formula for the sub-laplacian on a quaternionic contact manifold. With the help of this formula we establish a version of Lichnerowicz’ theorem giving a lower bound of the eigenvalues of the sub-Laplacian under a lower bound on the Sp(n)Sp(1) components of the qc-Ricci curvature. It is shown that in the case of a 3-Sasakian manifold the l...
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