Abstract
After reviewing few known facts regarding KdV equation as an Euler equation in the coadjoint orbit of the Virasoro–Bott group we are able to establish an interesting connection between the projective vector field, a vector field leaving fixed a given projective connection, and the C. Neumann system using the idea of Knörrer and Moser. We show that certain quadratic function of a projective field satisfies C. Neumann system.
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