PROLONGATIONS OF GEOMETRIC OVERDETERMINED SYSTEMS

By T. Branson, Andreas Čap, Michael Eastwood, Rod A. Gover. 2004

78 citations recorded by the source corpus.

We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on the dimension of the solution space.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6de6ef218cac2bb0be77ce8cf6c7a2cf10c0f821

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Michael Eastwood
2. V. Matveev
3. S. Benenti

In Computational Theory and Mathematics

1. Michael Eastwood
2. V. Matveev

In Statistical and Nonlinear Physics

1. V. Matveev
2. Michael Eastwood
3. Mikhail A. Vasiliev
4. X. Bekaert
5. M. Grigoriev

Citations in the corpus

• Notes on Projective Differential Geometry (2008, methodology): “This is part of Theorem 6.1 but is proved directly in [ 5 ] using Lie algebra cohomology (an instance of the 'BGG machinery') to construct explicit finite-type prolongations.”
• Metric Connections in Projective Differential Geometry (2008, background): “According to [2], this equation is of finite-type and may be prolonged to a closed system as follows.”