Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem

Details Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem

2006-11-22

arxiv.org/abs/math/0611658v5

Mathematics

Differential Geometry

51 pages, LaTeX 2e, 10pt, corrected Theorem 4.9 and Proposition 8.1

Scientific paper

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.

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