| EPSRC Reference: |
GR/M16825/01 |
| Title: |
THE GEOMETRY OF THE 2-DIMENSIONAL TODA EQUATIONS |
| Principal Investigator: |
Bolton, Dr J |
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| Department: |
Mathematical Sciences |
| Organisation: |
Durham, University of |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
10 July 1999 |
Ends: |
09 October 2001 |
Value (£): |
23,160
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Physics |
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The proposal concerns certain minimal surfaces having a high degree of symmetry. These surfaces, which are the analogues of soap films in 3-dimensional space, are solutions to a variational problem described by the Toda equations, an elliptic system of partial differential equations having many remarkable properties. In particular they are the equations of motion of an integrable Hamiltonian dynamical system and have received extensive study from applied mathematics.The geometrical aspects of these minimal surfaces have received much less attention and we will investigate them using various techniques. In addition to established methods from holomorphic function theory and the theory of Lie algebras and homogeneous spaces, we will exploit more recent developments in the use of loop group techniques in the theory of integrable systems. Problems to be addressed include:(i) a geometrical characterisation of these surfaces;(ii) the relation between the Toda system and the geometry of the corresponding surfaces;(iii) determination of criteria for two such surfaces to be related by a rigid motion of the ambient space;(iv) determination of explicit formulae for these surfaces;(v) the geometry of the totality of all such surfaces in interesting special cases.
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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 |
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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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