Proof of the Projective Lichnerowicz Conjecture for Pseudo-Riemannian Metrics with Degree of Mobility Greater than Two

@article{Kiosak2010ProofOT,
  title={Proof of the Projective Lichnerowicz Conjecture for Pseudo-Riemannian Metrics with Degree of Mobility Greater than Two},
  author={Volodymyr A. Kiosak and Vladimir Sergeevich Matveev},
  journal={Communications in Mathematical Physics},
  year={2010},
  volume={297},
  pages={401-426}
}
Degree of mobility of a (pseudo-Riemannian) metric is the dimension of the space of metrics geodesically equivalent to it. We prove that complete metrics on (n≥ 3)−dimensional manifolds with degree of mobility ≥ 3 do not admit complete metrics that are geodesically equivalent to them, but not affinely equivalent to them. As the main application we prove an important special case of the pseudo-Riemannian version of the projective Lichnerowicz conjecture stating that a complete manifold admitting… CONTINUE READING

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