Contents
Chapter 1. Introduction 1
Chapter 2. Quaternionic contact structures and the Biquard connection 7
Chapter 3. The torsion and curvature of the Biquard connection 13
3.1. The torsion tensor 13
3.2. The Curvature Tensor 18
Chapter 4. QC-Einstein quaternionic contact structures 23
4.1. The Bianchi identities 24
4.2. Examples of qc-Einstein structures 28
4.3. Proof of Theorem 1.3 31
Chapter 5. Conformal transformations of a qc-structure 37
5.1. Conformal transformations preserving the qc-Einstein condition 38
5.2. Quaternionic Heisenberg group. Proof of Theorem 1.1 39
Chapter 6. Special functions and pseudo-Einstein quaternionic contact
structures 47
6.1. Quaternionic pluriharmonic functions 47
6.2. Quaternionic pluriharmonic functions on hypercomplex manifold 51
6.3. The hypersurface case 53
6.4. Anti-CRF functions on Quaternionic contact manifold 55
Chapter 7. Infinitesimal Automorphisms 63
7.1. 3-contact manifolds 63
7.2. QC vector fields 65
Chapter 8. Quaternionic contact Yamabe problem 71
8.1. The Divergence Formula 71
8.2. Partial solutions of the qc-Yamabe problem 72
8.3. Proof of Theorem 1.2 74
Acknowledgements 75
Bibliography 77
Index 81
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