ORPP logo
Image from Google Jackets

Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society SeriesPublisher: Providence : American Mathematical Society, 2014Copyright date: ©2014Edition: 1st edDescription: 1 online resource (94 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470417222
Subject(s): Genre/Form: Additional physical formats: Print version:: Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe ProblemDDC classification:
  • 516.3/62
LOC classification:
  • QA649 .I93 2014
Online resources:
Contents:
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Quaternionic contact structures and the Biquard connection -- Chapter 3. The torsion and curvature of the Biquard connection -- 3.1. The torsion tensor -- 3.2. The Curvature Tensor -- Chapter 4. QC-Einstein quaternionic contact structures -- 4.1. The Bianchi identities -- 4.2. Examples of qc-Einstein structures -- 4.3. Proof of Theorem 1.3 -- Chapter 5. Conformal transformations of a qc-structure -- 5.1. Conformal transformations preserving the qc-Einstein condition -- 5.2. Quaternionic Heisenberg group. Proof of Theorem 1.1 -- Chapter 6. Special functions and pseudo-Einstein quaternionic contact structures -- 6.1. Quaternionic pluriharmonic functions -- 6.2. Quaternionic pluriharmonic functions on hypercomplex manifold -- 6.3. The hypersurface case -- 6.4. Anti-CRF functions on Quaternionic contact manifold -- Chapter 7. Infinitesimal Automorphisms -- 7.1. 3-contact manifolds -- 7.2. QC vector fields -- Chapter 8. Quaternionic contact Yamabe problem -- 8.1. The Divergence Formula -- 8.2. Partial solutions of the qc-Yamabe problem -- 8.3. Proof of Theorem 1.2 -- Acknowledgements -- Bibliography -- Index -- Back Cover.
Summary: 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.
Tags from this library: No tags from this library for this title. Log in to add tags.
Star ratings
    Average rating: 0.0 (0 votes)
No physical items for this record

Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Quaternionic contact structures and the Biquard connection -- Chapter 3. The torsion and curvature of the Biquard connection -- 3.1. The torsion tensor -- 3.2. The Curvature Tensor -- Chapter 4. QC-Einstein quaternionic contact structures -- 4.1. The Bianchi identities -- 4.2. Examples of qc-Einstein structures -- 4.3. Proof of Theorem 1.3 -- Chapter 5. Conformal transformations of a qc-structure -- 5.1. Conformal transformations preserving the qc-Einstein condition -- 5.2. Quaternionic Heisenberg group. Proof of Theorem 1.1 -- Chapter 6. Special functions and pseudo-Einstein quaternionic contact structures -- 6.1. Quaternionic pluriharmonic functions -- 6.2. Quaternionic pluriharmonic functions on hypercomplex manifold -- 6.3. The hypersurface case -- 6.4. Anti-CRF functions on Quaternionic contact manifold -- Chapter 7. Infinitesimal Automorphisms -- 7.1. 3-contact manifolds -- 7.2. QC vector fields -- Chapter 8. Quaternionic contact Yamabe problem -- 8.1. The Divergence Formula -- 8.2. Partial solutions of the qc-Yamabe problem -- 8.3. Proof of Theorem 1.2 -- Acknowledgements -- Bibliography -- Index -- Back Cover.

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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

There are no comments on this title.

to post a comment.

© 2024 Resource Centre. All rights reserved.