ArticleOriginal scientific text
Title
On the existence of connections with a prescribed skew-symmetric Ricci tensor
Authors ,
Abstract
We study the so-called inverse problem. Namely, given a prescribed skew-symmetric Ricci tensor we find (locally) a respective linear connection.
Keywords
Linear connection, Ricci tensor
Bibliography
- Dusek, Z., Kowalski, O., How many are Ricci flat affine connections with arbitrary torsion?, Publ. Math. Debrecen 88 (3-4) (2016), 511-516.
- Gasqui, J., Connexions a courbure de Ricci donnee, Math. Z. 168 (2) (1979), 167-179.
- Gasqui, J., Sur la courbure de Ricci d’une connexion lineaire, C. R. Acad. Sci. Paris Ser A–B 281 (11) (1975), 389-391.
- Kobayashi, S., Nomizu, K., Foundation of Differential Geometry, Vol. I, J. Wiley-Interscience, New York, 1963.
- Opozda, B., Mikulski, W. M., The Cauchy-Kowalevski theorem applied for counting connections with a prescribed Ricci tensor, Turkish J. Math. 42 (2) (2018), 528-536.