The Almost Schur Lemma in Quaternionic Contact Geometry

2022/04/09 by Stefan Ivanov, Ivanov, Stefan, Alexander Petkov +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2204.04482

openalex publication_date 2022/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish quaternionic contact (qc) versions of the so called Almost Schur Lemma, which give estimations of the qc scalar curvature on a compact qc manifold to be a constant in terms of the norm of the [-1]-component and the norm of the trace-free part of the [3]-component of the horizontal qc Ricci tensor and the torsion endomorphism, under certain positivity conditions.

Related

• The CR Almost Schur Lemma and the positivity conditions
• The topology of quaternionic contact manifolds
• A generalization of almost Schur lemma on CR manifolds
• Quaternionic contact Einstein manifolds
• Quaternionic contact structure with integrable complementary distribution