It is shown that for every multidimensional metric in the multiply-warped product form M¯ = K ×f1 M1 ×f2 M2 with warp functions f1, f2, associated to the submanifolds M1, M2 of dimensions n1, n2 respectively, one can find the corresponding Einstein equations G¯AB = −Λ¯¯gAB, with cosmological constant Λ, which are reducible to the ¯ Einstein equations Gαβ = −Λ1gαβ and Gij = −Λ2hij on the submanifolds M1, M2, with cosmological constants Λ1 and Λ2, respectively, where Λ, Λ ¯ 1 and Λ2 are functions of f1, f2 and n1, n2.
