Generalized orthotoric Kahler surfaces

Abstract

In this paper we describe QCH Kähler surfaces $(M,g,J)$ of generalized orthotoric type. We introduce a distinguished orthonormal frame on $(M,g)$ and give the structure equations for $(M,g,J)$. In the case when $I$ is conformally Kähler and $(M,g,J)$ is not hyperkähler we integrate these structure equations and rediscover the orthotoric Kähler surfaces. We also investigate the hyperkäler case. We prove in a simple way that if $(M,g,J)$ is a hyperkähler surface with a degenerate Weyl tensor $W^{-}$ (i.e. QCH hyperkähler surface) then among all hyperkäler structures on $(M,g)$ there exists a Kähler structure $J_0$ such that $(M,g,J_0)$ is of Calabi type or of orthotoric type.

References in corpus (4)

• Four--Dimensional Metrics Conformal to Kahler
• Kahler surfaces with quasi-constant holomorphic curvature
• Semi-symmetric Kahler surfaces
• Complex foliations and Kahler QCH surfaces