Brunella, Marco Locally conformally Kähler metrics on Kato surfaces. (English) Zbl 1227.32026 Nagoya Math. J. 202, 77-81 (2011). A Kato surface, or a surface with a global spherical shell, cannot be Kähler since its first Betti number is odd. In this work, the author shows that every Kato surface admits a locally conformally Kähler metric. As a consequence, the universal covering of a Kato surface is Kähler. Reviewer: Gabriela Paola Ovando (Rosario) Cited in 16 Documents MSC: 32J15 Compact complex surfaces 32Q15 Kähler manifolds 32Q30 Uniformization of complex manifolds Keywords:Kato surfaces; conformally Kähler surfaces; compact complex surfaces PDFBibTeX XMLCite \textit{M. Brunella}, Nagoya Math. J. 202, 77--81 (2011; Zbl 1227.32026) Full Text: DOI arXiv References: [1] F. A. Belgun, On the metric structure of non-Kähler complex surfaces , Math. Ann. 317 (2000), 1-40. · Zbl 0988.32017 · doi:10.1007/s002080050357 [2] M. Brunella, Locally conformally Kähler metrics on certain non-Kählerian surfaces , Math. Ann. 346 (2010), 629-639. · Zbl 1196.32015 · doi:10.1007/s00208-009-0407-8 [3] G. Dloussky, Structure des surfaces de Kato , Mém. Soc. Math. France (N.S.), no. 14 (1984). · Zbl 0543.32012 [4] M. Kato, “Compact complex manifolds containing ‘global’ spherical shells” in Proceedings of the International Symposium on Algebraic Geometry (Kyoto, 1977) , Kinokuniya, Tokyo, 1978, 45-84. · Zbl 0379.32023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.