Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem
A. L. Carey · V. Gayral · A. Rennie · F. A. Sukochev
Aug 2014 · American Mathematical Soc.
Ebook
82
Pages
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About this ebook
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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