Pseudo-riemannian manifolds with commuting jacobi operators

  title={Pseudo-riemannian manifolds with commuting jacobi operators},
  author={Miguel Brozos-V{\'a}zquez and Peter Gilkey},
  journal={Rendiconti del Circolo Matematico di Palermo},
We study the geometry of pseudo-Riemannian manifolds which are Jacobi-Tsankov, i.e. ℊ(x)ℊ(y)=ℊ(y)ℊ(x) for allx, y. We also study manifolds which are 2-step Jacobi nilpotent, i.e. ℊ(x)ℊ(y)=0 for allx, y. 

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