arXiv subjects
Publications and source records attributed to Włodzimierz Jelonek.
In this paper we prove that some well known Kähler surfaces with zero scalar curvature are QCH Kähler. We prove that family of generalized Taub-Nut Kähler surfaces parametrized by $k\in[-1,1]$ is of orthotoric type for $k\in(-1,1)$ and of Calabi type for $k\in\{-1,1\}$ and the Burn's metric is of Calabi type.
We show that the manifold $X=S^2\times S^3$ has infinitely many structures of a fiber bundle over the base $B=S^2.$ In fact for every lens space $L(p,1)$ there is a fibration $L(p,1)\to X\to B.$
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.
In this paper we give classification of Kähler surfaces of generalized Calabi type.
The aim of this paper is to classify compact, simply connected Kähler manifolds which admit J-invariant Killing tensor with two eigenvalues of multiplicity 2 and n-2 and with constant eigenvalue corresponding to 2-dimensional eigendistribution.