Curvature homogeneous signature (2,2) manifolds

Details Curvature homogeneous signature (2,2) manifolds Curvature homogeneous signature (2,2) manifolds

2004-08-23

arxiv.org/abs/math/0408316v1

Mathematics

Differential Geometry

Scientific paper

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.

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