A nonlinear superposition principle admitted by coupled Riccati equations of the projective type

A definite theorem due to Lie which group theoretically characterizes those systems of ordinary differential equations which possess nonlinear superposition principles is employed along with an observation by Lie on the exponentiated form of a fibered Lie algebra to obtain an explicit expression for the Vessiot-Guldberg-Lie nonlinear superposition principle admitted by n-coupled Riccati equations of the projective type. This also, immediately, yields an explicit expression for the generalized cross-ratio for the projective group in n-dimensions.Reported at the Georgia Workshop in Mathematical Physics, November 26–28, 1979, UGA, Athens, Georgia.