Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem

Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem

2014 | ISBN-10: 0821898434 | 82 Pages | PDF | 0,7 MB

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 manifolds. All conformal transformations 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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