The codegree density (F) of an r-graph F is the largest number such that there are F-free r-graphs G on n vertices such that every set of r - 1 vertices is contained in at least (γ−o(1))nedges.F ortheF anoplaneP G(2, 2), Mubayishowedthatγ(P G(2, 2)) = 1/2.F orgeneralprojectivegeometriesweobtaintheupperboundγ(P G(m, q))1/m.W eshowthatequalityholdswheneverm = 2andqisodd, andwheneverm = 3andqis2or3.W ealsogiveexamplesofr−graphswithcodegreedensitiesequalto1− 1/kforallrandk.