Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem

2006/11/22 by Stefan Ivanov, Ivan Minchev, Ivanov, Stefan +3 · 6 citations
Mathematics · #53C21 #53C26 #53D10 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0611658

openalex publication_date 2006/11/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolods. All conformal deformations sending the standard flat torsion-free quaternionic contact structure on the quaternionic Heisenberg group to a quaternionic contact structure with vanishing torsion of the Biquard connection are explicitly described. A '3-Hamiltonian form' of infinitesimal conformal automorphisms of quaternionic contact structures is presented.

Citations

• Metriques de Carnot-Caratheodory et Quasiisometries des Espaces Symetriques de rang un

Cited by

• The twistor space of a quaternionic contact manifold
• Extremals for the Sobolev inequality on the seven dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem
• On the existence of local quaternionic contact geometries
• Heat kernel asymptotics for quaternionic contact manifolds
• A heat equation on a quaternionic contact manifold
• The topology of quaternionic contact manifolds

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