| EPSRC Reference: |
GR/L94031/01 |
| Title: |
ANALYSIS OF ANTI-SELF-DUAL METRICS ON COMPACT 4-MANIFOLDS |
| Principal Investigator: |
Singer, Professor M |
| Other Investigators: |
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| Department: |
Sch of Mathematics |
| Organisation: |
University of Edinburgh |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 March 1998 |
Ends: |
29 February 2000 |
Value (£): |
79,001
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Some of the most important current problems in differential geometry are concerned with the existence and uniqueness of optimal Riemannian metrics on smooth closed manifolds. In dimension 4, the anti-self-dual (ASD) metrics provide such an optimal class, and this proposal is devoted to a study of existence and uniqueness questions for these metrices. To be more specific, a general theory of ASD orbifolds will be developed, using analytical methods (non-linear elliptic partial differential equations). This theory will include general existence theorems and results relating the moduli spaces of the summands to the moduli space of ASD metrics on the connected sum. The existence theorem will be used to construct new examples of ASD metrics by taking connected sums of known orbifolds. (Examples of such orbifiolds are plenty). Variations on this theme will also be considered: connected sums of ASD Hermitian manifolds or orbifolds for example. This research builds on previous work of several authors including the Principal Investigator and named RA.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ed.ac.uk |