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Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem

Stefan Ivanov Univ. of Sofia and Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria
Ivan Minchev University of Sofia, Sofia, Bulgaria
Dimiter Vassilev University of New Mexico, Albuquerque
Available Formats:
Electronic ISBN: 978-1-4704-1722-2
Product Code: MEMO/231/1086.E
List Price: $65.00 MAA Member Price:$58.50
AMS Member Price: $39.00 Click above image for expanded view Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem Stefan Ivanov Univ. of Sofia and Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria Ivan Minchev University of Sofia, Sofia, Bulgaria Dimiter Vassilev University of New Mexico, Albuquerque Available Formats:  Electronic ISBN: 978-1-4704-1722-2 Product Code: MEMO/231/1086.E  List Price:$65.00 MAA Member Price: $58.50 AMS Member Price:$39.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 2312014; 82 pp
MSC: Primary 53;

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.

• Chapters
• 1. Introduction
• 2. Quaternionic contact structures and the Biquard connection
• 3. The torsion and curvature of the Biquard connection
• 4. QC-Einstein quaternionic contact structures
• 5. Conformal transformations of a qc-structure
• 6. Special functions and pseudo-Einstein quaternionic contact structures
• 7. Infinitesimal Automorphisms
• 8. Quaternionic contact Yamabe problem
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Volume: 2312014; 82 pp
MSC: Primary 53;

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.

• Chapters
• 1. Introduction
• 2. Quaternionic contact structures and the Biquard connection
• 3. The torsion and curvature of the Biquard connection
• 4. QC-Einstein quaternionic contact structures
• 5. Conformal transformations of a qc-structure
• 6. Special functions and pseudo-Einstein quaternionic contact structures
• 7. Infinitesimal Automorphisms
• 8. Quaternionic contact Yamabe problem
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