| 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 231; 2014; 82 ppMSC: 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.
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Table of Contents
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Chapters
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1. Introduction
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2. Quaternionic contact structures and the Biquard connection
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3. The torsion and curvature of the Biquard connection
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4. QC-Einstein quaternionic contact structures
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5. Conformal transformations of a qc-structure
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6. Special functions and pseudo-Einstein quaternionic contact structures
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7. Infinitesimal Automorphisms
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8. Quaternionic contact Yamabe problem
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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
