The spectral geometry of the Weyl conformal tensor

2003/10/15 by N. Blazic, Novica Blažić, P. Gilkey +9 · 2 citations
Mathematics · Physics and Astronomy · #53C50 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:53C50

paper · pdf · doi:10.48550/arxiv.math/0310226

arxiv created 2003/10/15 · openalex publication_date 2003/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Manifolds which are Ivanov-Petrova or k-Stanilov

Cited by

• The Spectral Geometry of the Riemann Curvature Operator in the Higher Signature Setting
• Stanilov-Tsankov-Videv Theory

Related

• The spectral geometry of the Riemann curvature tensor
• Conformally Osserman manifolds
• Osserman manifolds and Weyl-Schouten Theorem for rank-one symmetric spaces
• Conformally Osserman manifolds and self-duality in Riemannian geometry
• The Spectral Geometry of the Riemann Curvature Operator in the Higher Signature Setting