Complete Einstein metrics are geodesically rigid

@inproceedings{Kiosak2008CompleteEM,
  title={Complete Einstein metrics are geodesically rigid},
  author={Volodymyr Kiosak and Vladimir S. Matveev},
  year={2008}
}
We prove that every complete Einstein (Riemannian or pseudo-Riemannian) metric g is geodesically rigid: if any other complete metric ḡ has the same (unparametrized) geodesics with g, then the Levi-Civita connections of g and ḡ coincide. MSC: 83C10, 53C27, 53A20, 53B21, 53C22, 53C50, 70H06, 58J60, 53D25,70G45. 

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