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We study a generalized Einstein theory with the following two criteria:{\iti}) on the solar scale, it must be consistent with the classical tests ofgeneral relativity, {\it ii}) on the galactic scale, the gravitationalpotential is a sum of Newtonian and Yukawa potentials so that it may explainthe flat rotation curves of spiral galaxies. Under these criteria, we find thatsuch a generalized Einstein action must include at least one scalar field andone vector field as well as the quadratic term of the scalar curvature.Comment: 13 pages, Latex, SLAC-PUB-596

Generalized Einstein theory on solar and galactic scales