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We study the affine quasi-Einstein equation, a second order linearhomogeneous equation, which is invariantly defined on any affine manifold. Weprove that the space of solutions is finite-dimensional, and its dimension is astrongly projective invariant. Moreover the maximal dimension is shown to beachieved if and only if the manifold is strongly projectively flat.

A natural linear equation in affine geometry: the affine quasi-Einstein equation