Neculai Papaghiuc
Abstract
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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).
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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).
Key concepts: Tangent bundle, Mathematics, Ricci curvature, Fundamental theorem of Riemannian geometry, Unit tangent bundle, Levi-Civita connection, Pure mathematics, Riemannian manifold