How many linear connections are there with a prescribed Ricci tensor? The question is answered in the analytic case by using the Cauchy-Kowalevski theorem
Linear connection, Ricci tensor, Cauchy-Kowalevski theorem
OPOZDA, BARBARA and MIKULSKI, WLODZIMIERZ M.
"The Cauchy-Kowalevski theorem applied for counting connections with a prescribed Ricci tensor,"
Turkish Journal of Mathematics: Vol. 42:
2, Article 9.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss2/9