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 iii
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