| EPSRC Reference: |
GR/A00188/01 |
| Title: |
AF: MONOPOLES AND QUATERNIONIC GEOMETRY |
| Principal Investigator: |
Bielawski, Professor R |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
School of Mathematics & Statistics |
| Organisation: |
University of Glasgow |
| Scheme: |
Advanced Fellowship (Pre-FEC) |
| Starts: |
01 April 2000 |
Ends: |
30 September 2003 |
Value (£): |
118,065
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
The aim of the project is to further the understanding of quaternionic Riemannian geometry (meaning hyperkaehler, quaternion-Kaehler and 3-Sasakian geometry) and its links with mathematical physics, in particular the theory of magnetic monopoles. Specific topics include: topology of hyperkaehler and 3-Sasakian quotients; classification of hyperkaehler manifolds with large symmetry group; existence of compact non-symettric quaternion-Kaehler manifolds; properties of hyperkaekler manifolds obtained by the (generalised) Legendre transform; new constructions of hyperkaehler and hyper-complex manifolds. The second complementary part of the project is the study of certain specific properties of natural hyperkaehler metrics on moduli spaces of Euclidean monopoles, which are of interest from both mathematical and physical point of view: asymptotics; construction of these metrics using the generalised Legendre transform; existence of closed geodesics. Further problems include the relationship between monopoles and skyrmiona, and the existence and construction of quaternion-Kaehler metrics on moduli spaces of hyperbolic monopoles.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.gla.ac.uk |