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Published online by Cambridge University Press: 17 December 2014
Given the pair (P, η) of (0,2) tensors, where η defines a volume element, we consider a new variational problem varying η only. We then have Einstein metrics and slant immersions as critical points of the 1st variation. We may characterize Ricci flat metrics and Lagrangian submanifolds as stable critical points of our variational problem.