A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold
Volume 87 / 2001
Colloquium Mathematicum 87 (2001), 227-233
MSC: 53C50, 53C07.
DOI: 10.4064/cm87-2-8
Abstract
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).
