top
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).
Neculai Papaghiuc. "A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold." Colloquium Mathematicae 87.2 (2001): 227-233. <http://eudml.org/doc/283728>.
@article{NeculaiPapaghiuc2001, 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).}, author = {Neculai Papaghiuc}, journal = {Colloquium Mathematicae}, keywords = {pseudo-Riemannian manifold; tangent bundle; prolongation of metrics; Ricci flat metric}, language = {eng}, number = {2}, pages = {227-233}, title = {A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold}, url = {http://eudml.org/doc/283728}, volume = {87}, year = {2001}, }
TY - JOUR AU - Neculai Papaghiuc TI - A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold JO - Colloquium Mathematicae PY - 2001 VL - 87 IS - 2 SP - 227 EP - 233 AB - 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). LA - eng KW - pseudo-Riemannian manifold; tangent bundle; prolongation of metrics; Ricci flat metric UR - http://eudml.org/doc/283728 ER -