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Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem


About this Title

Stefan Ivanov, Ivan Minchev and Dimiter Vassilev

Publication: Memoirs of the American Mathematical Society
Publication Year: 2014; Volume 231, Number 1086
ISBNs: 978-0-8218-9843-7 (print); 978-1-4704-1722-2 (online)
DOI: http://dx.doi.org/10.1090/memo/1086
Published electronically: January 31, 2014
Keywords:Yamabe equation, quaternionic contact structures

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Table of Contents


Chapters

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

Abstract


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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