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arXiv · 1606.07701

Holonomy classification of Lorentz-Kähler manifolds

Anton S. Galaev
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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.

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Anton S. Galaev. 2018-08-20. Holonomy classification of Lorentz-Kähler manifolds. https://doi.org/10.1007/s12220-018-0027-1

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