The spectral geometry of the Weyl conformal tensor
Volume 69 / 2005
Banach Center Publications 69 (2005), 195-203
MSC: Primary 53B20.
DOI: 10.4064/bc69-0-15
Abstract
We study when the Jacobi operator associated to the Weyl conformal curvature tensor has constant eigenvalues on the bundle of unit spacelike or timelike tangent vectors. This leads to questions in the conformal geometry of pseudo-Riemannian manifolds which generalize the Osserman conjecture to this setting. We also study similar questions related to the skew-symmetric curvature operator defined by the Weyl conformal curvature tensor.
