Conformally Osserman manifolds and conformally complex space forms

Details Conformally Osserman manifolds and conformally complex space forms Conformally Osserman manifolds and conformally complex space forms

2003-11-16

arxiv.org/abs/math/0311263v1

Mathematics

Differential Geometry

Scientific paper

We characterize manifolds which are locally conformally equivalent to either complex projective space or to its negative curvature dual in terms of their Weyl curvature tensor. As a byproduct of this investigation, we classify the conformally complex space forms if the dimension is at least 8. We also study when the Jacobi operator associated to the Weyl conformal curvature tensor of a Riemannian manifold has constant eigenvalues on the bundle of unit tangent vectors and classify such manifolds which are not conformally flat in dimensions congruent to 2 mod 4.

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