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arXiv · 2608.27022

On LCK Geometry of Gauduchon Connections

Giuseppe Barbaro·Alexandra Otiman
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Abstract

It is not a priori clear which of the Gauduchon connections is better suited to LCK and Vaisman manifolds. We thus investigate the geometry of these connections through Einstein problems and more general analytic and cohomological conditions on their Ricci tensors. Our results single out the Bismut connection as the privileged one for the non-K\"ahler lcK and Vaisman geometry. We therefore study the {second-Bismut--Einstein} equation and provide a characterization of these structures on Hopf manifolds.

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Giuseppe Barbaro, Alexandra Otiman. 2026-08-27. On LCK Geometry of Gauduchon Connections. https://arxiv.org/abs/2608.27022

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