Holonomy classification of Lorentz-Kähler manifolds

Abstract

The classification problem for holonomy of pseudo-Riemannian manifolds is actual and open. In the present paper, holonomy algebras of Lorentz-Kähler 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-Kähler symmetric spaces is reviewed.

the final version accepted to The Journal of Geometric Analysis

References in corpus (2)

• Holonomy groups of Lorentzian manifolds
• Holonomy groups of pseudo-quaternionic-Kählerian manifolds of non-zero scalar curvature

Cited by in corpus (1)

• Local Type III metrics with holonomy in ${\mathrm{G}}_2^{\ast }$