The Obata first eigenvalue theorems on a seven dimensional quaternionic\n contact manifold

2020/12/31 by Abdelrahman Mohamed, Mohamed, Abdelrahman, Dimiter Vassilev +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #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.2012.15767

openalex publication_date 2020/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a compact quaternionic contact manifold of dimension seven that\nsatisfies a Lichnerowicz-type lower Ricci-type bound and has the P-function\nof any eigenfunction of the sub-Laplacian non-negative achieves its smallest\npossible eigenvalue only if the structure is qc-Einstein. In particular, under\nthe stated conditions, the lowest eigenvalue is achieved if and only if the\nmanifold is qc-equivalent to the standard 3-Sasakian sphere.\n

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