Pseudo-Riemannian manifolds with Commuting Jacobi Operators

Abstract

We study the geometry of pseudo-Riemannian manifolds which are Jacobi--Tsankov, i.e. J(x)J(y)=J(y)J(x) for all tangent vectors x and y. We also study manifolds which are 2-step Jacobi nilpotent, i.e. J(x)J(y)=0 for all tangent vectors x and y.

Cited by in corpus (2)

• Examples of signature (2,2) manifolds with commuting curvature operators
• Jacobi--Tsankov manifolds which are not 2-step nilpotent