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arXiv · 1001.0936

LCK metrics on elliptic principal bundles

Victor Vuletescu
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Abstract

For elliptic principal bundles $π:X\ra B$ over Kähler manifolds it was shown by Blanchard that $X$ has a Kähler metric if and only both Chern classes (with real coefficients) of $π$ vanish. For some elliptic principal bundles, when the span of these Chern classes is 1-dimensional, it was shown by Vaisman that $X$ carry locally conformally Kähler (LCK, for short) metrics. We show that in the case when the Chern classes are linearly independent, $X$ carries no LCK metric.

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Victor Vuletescu. 2010-01-06. LCK metrics on elliptic principal bundles. https://arxiv.org/abs/1001.0936

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