Conformally Osserman manifolds and self-duality in Riemannian geometry

Novica Blazic; Peter Gilkey

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arXiv · math/0504498

Conformally Osserman manifolds and self-duality in Riemannian geometry

Novica Blazic·Peter Gilkey

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Abstract

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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Novica Blazic, Peter Gilkey. 2005-04-25. Conformally Osserman manifolds and self-duality in Riemannian geometry. https://arxiv.org/abs/math/0504498

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