Prolongations of Geometric Overdetermined Systems

Abstract

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.

22 pages. In the second version, a comparison with the classical theory of prolongations was added. In this third version more details were added concerning our construction and especially the use of Kostant's computation of Lie algebra cohomology