| EPSRC Reference: |
GR/S34304/01 |
| Title: |
Cartan connections and third order ordinary differential equations |
| Principal Investigator: |
Hughston, Professor LP |
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| Department: |
Mathematics |
| Organisation: |
Kings College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
05 May 2003 |
Ends: |
04 August 2003 |
Value (£): |
8,713
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
| 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 aim of this research is to study the differential geometry of third order ODES in two independent variables and one dependent variable. The main method that will be used is Carton's method of equivalence under three types of transformations of the independent and dependent variables. These are respectively contact, pant and fibre preserving transformations. In each case the full set of invariants of the ODE will be found and used to distinguish inequivalent sets of equations. This classification of the equations under these transformations will extend and rune the pioneering work by E. Cartan and S. S. Chem. The geometrical and physical significance of the dWerent branches of the classification will also be studied, and the associated Cartan connections will be established. The classes of third order ODEs that are known to be in one- to -one correspondence with three dimensional conformal Lorentzian geometries, and Laentzian Weyl geometrces, will be further investigated.. These classes and the invariarnts of the equations will be related to, and interpreted in terms of, these geometrccs and associated geometrical objects. New geometrical insights resulting from this approach, and relationships to completely integrable systems of partial differential equations, will be explored.
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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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