The sharp lower bound of the first eigenvalue of the sub-Laplacian on a\n quaternionic contact manifold in dimension seven

2012/10/25 by Stefan Ivanov, Ivanov, Stefan, Alexander Petkov +3
Mathematics · #53C26 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1210.6932

openalex publication_date 2012/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A version of Lichnerowicz' theorem giving a lower bound of the eigenvalues of\nthe sub-Laplacian under a lower bound on the Sp(1)Sp(1) component of the\nqc-Ricci curvature on a compact seven dimensional quaternionic contact manifold\nis established. It is shown that in the case of a seven dimensional compact\n3-Sasakian manifold the lower bound is reached if and only if the quaternionic\ncontact manifold is a round 3-Sasakian sphere.\n

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