Publication details
Holonomy Classification of Lorentz-Kahler Manifolds
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Geometric Analysis |
| Citation | |
| Doi | https://doi.org/10.1007/s12220-018-0027-1 |
| Keywords | Lorentz-Kahler manifold; Holonomy group; Complex Walker coordinates; Complex pp-wave; Symmetric space; Space of oriented lines |
| Description | The classification problem for holonomy of pseudo-Riemannian manifolds is actual and open. In the present paper, holonomy algebras of Lorentz-Kahler manifolds are classified. A simple construction of a metric for each holonomy algebra is given. Complex Walker coordinates are introduced and described using the potential. Complex pp-waves are characterized in terms of the curvature, holonomy, and the potential. Classification of Lorentz-Kahler symmetric spaces is reviewed. |