[图书][B] Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem
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 …
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 …
Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem
S Ivanov, I Minchev, D Vassilev - arXiv preprint math/0611658, 2006 - arxiv.org
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 …
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 …