A Note on the Liouville Equation

A. Grauel 1
  • 1 Fachbereich 6 der Universität-Gesamthochschule Paderborn

We study some geometrical features of the non-linear scattering equations [1]. From this we deduce the Liouville equation. For that we interpret the SL(2, ℝ)-valued elements of the matrices in the scattering equations as matrix-valued forms and calculate the curvature 2-form with respect to a basis of the Lie algebra. We obtain the Liouville equation if the curvature form is equal to zero

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