Curvature homogeneous signature (2,2) manifolds

2004/08/23 by C. Dunn, Dunn, C., P. Gilkey +3
Mathematics · Physics and Astronomy · #53B20 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:53B20

paper · pdf · doi:10.48550/arxiv.math/0408316

arxiv created 2004/08/23 · arxiv updated 2009/12/01

Abstract

We exhibit a family of generalized plane wave manifolds of signature (2,2). The geodesics in these manifolds extend for infinite time (i.e. they are complete), they are spacelike and timelike Jordan Osserman, and they are spacelike and timelike Jordan Ivanov-Petrova. Some are irreducible symmetric spaces. Some are homogeneous spaces but not symmetric. Some are 1-curvature homogeneous but not homogeneous. All are 0-modeled on the same irreducible symmetric space. We determine the Killing vector fields for these manifolds.

Related

• Generalized plane wave manifolds
• Curvature homogeneous pseudo-Riemannian manifolds which are not locally homogeneous
• Complete k-curvature homogeneous pseudo-Riemannian manifolds
• Complete k-curvature homogeneous pseudo-Riemannian manifolds 0-modeled on an indecomposible symmetric space
• Irreducible Killing and conformal Killing tensors on homogeneous plane waves