Geodesic
How many are projectable classical linear connections with a prescribed Ricci tensor
Filomat, Tome 35 (2021) no. 10, p. 3279

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DOI

How many are projectable classical linear connections with a prescribed Ricci tensor and a prescribed trace of torsion tensor on the total space of a fibered manifold? The questions are answered in the analytic case by using the Cauchy-Kowalevski theorem. In the C ∞ case, we answer how many are classical linear connections with a prescribed Ricci tensor on a 2-dimensional manifold. In the C ∞ case, we also deduce that any 2-form on the total space of a fibered manifold with at least 2-dimensional fibres can be realized locally as the Ricci tensor of a projectable classical linear connection
DOI : 10.2298/FIL2110279K
Classification : 35A10, 35Q99, 53B05, 53B20, 35G50
Keywords: projectable classical linear connection, Ricci tensor, Cauchy-Kowalevski theorem 
Jan Kurek; Włodzimierz M Mikulski; Mariusz Plaszczyk. How many are projectable classical linear connections with a prescribed Ricci tensor. Filomat, Tome 35 (2021) no. 10, p. 3279 . doi: 10.2298/FIL2110279K
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     title = {How many are projectable classical linear connections with a prescribed {Ricci} tensor},
     journal = {Filomat},
     pages = {3279 },
     year = {2021},
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     doi = {10.2298/FIL2110279K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2110279K/}
}
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