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We show that every Sasakian manifold in dimensions 2k + 1 is locally generated by a free real function of 2k variables. This function is a Sasakian analogue of the Kähler potential for the Kähler geometry. It is also shown that every locally Sasakian-Einstein manifold in 2k + 1 dimensions is generated by a locally Kähler-Einstein manifold in dimension 2k.
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Godliński et al. (2000) studied this question.
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