Conformally Osserman manifolds and self-duality in Riemannian geometry
Differential Geometry
2007-05-23 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.math/0504498,
title = {Conformally Osserman manifolds and self-duality in Riemannian geometry},
author = {Novica Blazic and Peter Gilkey},
journal= {arXiv preprint arXiv:math/0504498},
year = {2007}
}