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On LCK Geometry of Gauduchon Connections
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-Kähler 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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BibTeX
@misc{barbaro2026geometry,
title = {{On LCK Geometry of Gauduchon Connections}},
author = {Giuseppe Barbaro and Alexandra Otiman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.27022},
eprint = {2608.27022},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27022},
}
RIS
TY - UNPB
TI - On LCK Geometry of Gauduchon Connections
AU - Giuseppe Barbaro
AU - Alexandra Otiman
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2608.27022
UR - https://arxiv.org/abs/2608.27022
AB - 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-Kähler lcK and Vaisman geometry. We therefore study the {second-Bismut--Einstein} equation and provide a characterization of these structures on Hopf manifolds.
ER -