The spectral geometry of the Weyl conformal tensor

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.

References in corpus (1)

• Manifolds which are Ivanov-Petrova or k-Stanilov

Cited by in corpus (2)

• Conformally Osserman manifolds and self-duality in Riemannian geometry
• The Spectral Geometry of the Riemann Curvature Operator in the Higher Signature Setting