Estimating the eigenvalues on Quaternionic Kähler Manifolds

2004/05/20 by Yasushi Homma, Homma, Yasushi
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.math/0405384

32page. minor revision including new observations

openalex publication_date 2004/05/20 · arxiv created 2005/09/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study geometric first order differential operators on quaternionic Kähler manifolds. Their principal symbols are related to the enveloping algebra and Casimir elements for \Sp(1)\Sp(n). This observation leads to anti-symmetry of the principal symbols and Bochner-Weitzenböck formulas for operators. As an application, we estimate the first eigenvalues of them.

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