Geometric properties of neutral signature metrics on 4-dimensional nilpotent Lie groups

Abstract

The classification of left invariant metrics of neutral signature on the 4-dimensional nilpotent Lie groups is presented. Their geometry is extensively studied with special emphasis on the holonomy groups and projective equivalence. Additionally, we focus our attention on the Walker metrics. They appear as the underlying structure of metrics on the nilpotent Lie groups with degenerate center. Finally, we give complete description of the isometry groups.