A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold
Neculai Papaghiuc (2001)
Colloquium Mathematicae
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We consider a certain pseudo-Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g) and obtain necessary and sufficient conditions for the pseudo-Riemannian manifold (TM,G) to be Ricci flat (see Theorem 2).