• Corpus ID: 118859396

Conformally Osserman manifolds and self-duality in Riemannian geometry

@article{Blai2005ConformallyOM,
  title={Conformally Osserman manifolds and self-duality in Riemannian geometry},
  author={Novica Bla{\vz}i{\'c} and Peter Gilkey},
  journal={arXiv: Differential Geometry},
  year={2005}
}
We study the spectral geometry of the conformal Jacobi operator on a 4-dimensional Riemannian manifold (M,g). We show that (M,g) is conformally Osserman if and only if (M,g) is self-dual or anti self-dual. Equivalently, this means that the curvature tensor of (M,g) is given by a quaternionic structure, at least pointwise. 

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