Higher order Jordan Osserman Pseudo-Riemannian manifolds

Abstract

We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r,s) for certain values of (r,s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher order Osserman manifolds.

References in corpus (1)

• The Jordan normal form of higher order Osserman algebraic curvature tensors

Cited by in corpus (5)

• Complete curvature homogeneous pseudo-Riemannian manifolds
• Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds
• Pseudo-Riemannian manifolds with Commuting Jacobi Operators
• Manifolds with commuting Jacobi operators
• The Spectral Geometry of the Riemann Curvature Operator in the Higher Signature Setting