2003/02/04 by Peter Gilkey, P. Gilkey, Gilkey, P. +3
Mathematics · Physics and Astronomy · #53B20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53B20
paper · pdf · doi:10.48550/arxiv.math/0302044
arxiv created 2003/02/04 · openalex publication_date 2003/02/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Pseudo-Riemannian manifolds of balanced signature which are both spacelike and timelike Jordan Osserman nilpotent of order 2 and of order 3 have been constructed previously. In this short note, we shall construct pseudo-Riemannian manifolds of signature (2s,s) for any s (which is at least 2) which are spacelike Jordan Osserman nilpotent of order 3 but which are not timelike Jordan Osserman. Our example and techniques are quite different from known previously both in that they are not in neutral signature and that the manifolds constructed will be spacelike but not timelike Jordan Osserman.