EPSRC Reference: 
GR/N30941/01 
Title: 
PROJECTIVE DIFFERENTIAL GEOMETRY AND INTEGRABLE SYSTEMS 
Principal Investigator: 
Ferapontov, Professor E 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
School of Mathematics 
Organisation: 
Loughborough University 
Scheme: 
Standard Research (PreFEC) 
Starts: 
01 October 2000 
Ends: 
31 March 2002 
Value (£): 
61,989

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
The projective differential geometry of surfaces and line congruences was one of the most popular topics at the turn of the last century. As the proposer and his collaborators observed recently, many constructions of the classical period are extremely relevant to the modern theory of systems of conservation laws. Translated into the geometric setting, such basic concepts as the shock and rarefaction curves, the linearly degenerate systems and systems of Temple's class acquire a simple and descriptive interpretation in the language of line geometry.one of the aims of the project is to apply this geometric correspondence to the classification of systems of conservation laws with linear rarefaction curves, examples of which include the equations of chromatography in chemical kinetics and the equations of associativity in topological field theory. Geometrically, this problem is equivalent to the classification of congruences with planar developable surfaces.The second aim of the project is the description of surfaces possessing multiparameter families of projective deformations. Mathematically, this problem is equivalent to the description of commuting second order differential operators containing nontrivial electromagnetic terms. This makes the problem soluble by the existing methods of the modern soliton theory.

Key Findings 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.lboro.ac.uk 