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Abstract
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It is shown that for every multidimensional metric in the multiply warped product form M¯=K×f1M1×f2M2 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¯g¯AB, 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¯, Λ1 and Λ2 are functions of f1, f2 and n1, n2.
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