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Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem
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Artikel-Nr:
9781470417222
Einband:
PDF
Seiten:
82
Autor:
Stefan Ivanov
eBook Typ:
PDF
eBook Format:
PDF
Kopierschutz:
Adobe DRM [Hard-DRM]
Sprache:
Deutsch
Beschreibung:
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 "e;3-Hamiltonian form"e; of infinitesimal conformal automorphisms of quaternionic contact structures is presented.
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 "e;3-Hamiltonian form"e; of infinitesimal conformal automorphisms of quaternionic contact structures is presented.