Reduction of exterior differential systems with infinite dimensional symmetry groups

2008 ◽  
Vol 48 (2) ◽  
pp. 337-355 ◽  
Author(s):  
J. Pohjanpelto
Keyword(s):  
Symmetry Groups ◽  
Differential Systems ◽  
Exterior Differential Systems ◽  
Infinite Dimensional ◽  
Exterior Differential

DEGENERATE TORSION-FREE G3-CONNECTIONS

1998 ◽  
Vol 09 (08) ◽  
pp. 945-955 ◽  
Author(s):  
QUO-SHIN ChI
Keyword(s):  
Moduli Space ◽  
Technical Condition ◽  
Analytic Torsion ◽  
Differential Systems ◽  
Exterior Differential Systems ◽  
Infinite Dimensional ◽  
Exterior Differential ◽  
Finite Dimensional ◽  
Torsion Free

Using exterior differential systems (EDS), Bryant proved that the moduli space of nondegenerate analytic torsion-free G3-connections depends on four functions in three variables. Here nondegeneracy is a technical condition which imposes the nonvanishing everywhere of a certain determinant pertinent to a torsion-free G3-connection for EDS to carry through. The finite-dimensional moduli of homogeneous torsion-free G3-connections are degenerate examples, where the determinant vanishes identically. We establish in fact that the moduli space of analytic inhomogeneous degenerate torsion-free G3-connections is infinite-dimensional.

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