Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
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
Front Cover for Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem
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
Front Cover for Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem
Click above image for expanded view
  • Front Cover for Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem
  • Back Cover for Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem
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.

  • Table of Contents
     
     
    • 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
  • Request Review Copy
  • Get Permissions
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
Please select which format for which you are requesting permissions.