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arXiv · 1208.6518

On a question of Vaisman concerning complex surfaces

Massimiliano Pontecorvo
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Abstract

The last years have seen striking improvements on Vaisman's question about existence of locally conformally Kähler (lcK) metrics on compact complex surfaces. The aim of this paper is two-fold. We review results of different authors which, for all known examples of compact complex surfaces, give a complete answer to Vaisman's question. We also point out a relation between lcK surfaces and generalized Kähler geometry in four-dimension and prove a new result concerning generalized Kähler structures on Hyperbolic Inoue surfaces. We conclude with a simple observation on a question of Brunella.

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Massimiliano Pontecorvo. 2012-08-31. On a question of Vaisman concerning complex surfaces. https://arxiv.org/abs/1208.6518

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