Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem

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Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem is written by A. L. Carey and published by American Mathematical Soc.. It's available with International Standard Book Number or ISBN identification 0821898434 (ISBN 10) and 9780821898437 (ISBN 13).

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.