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Some Particular cases are explained in this paper
https://publi.math.unideb.hu/load_doc.php?p=551&t=papPapaghiuc - On an Einstein structure on the tanent bundle of a space form.
https://publi.math.unideb.hu/load_doc.php?p=551&t=pap
Some Particular cases are explained in Papaghiuc - On an Einstein structure on the tanent bundle of a space form.
Some Particular casecases are explained in this paper
Some Particular case are explained in this paper