Conformally Osserman manifolds and self-duality in Riemannian geometry

Details Conformally Osserman manifolds and self-duality in Riemannian geometry Conformally Osserman manifolds and self-duality in Riemannian geometry

2005-04-25

arxiv.org/abs/math/0504498v1

Mathematics

Differential Geometry

Scientific paper

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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