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- W4379924449 abstract "We complete the classification of six-dimensional strongly unimodular almost nilpotent Lie algebras admitting complex structures. For several cases we describe the space of complex structures up to isomorphism. As a consequence we determine the six-dimensional almost nilpotent solvmanifolds admitting an invariant complex structure and study the existence of special types of Hermitian metrics, including SKT, balanced, locally conformally Kahler, and strongly Gauduchon metrics. In particular, we determine new balanced solvmanifolds and confirm a conjecture by the first author and Vezzoni regarding SKT and balanced structures in the six-dimensional strongly unimodular almost nilpotent case. Moreover, we prove some negative results regarding complex structures tamed by symplectic forms, showing in particular that in every dimension such structures cannot exist on non-Kahler almost abelian Lie algebras." @default.
- W4379924449 created "2023-06-09" @default.
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- W4379924449 date "2023-06-06" @default.
- W4379924449 modified "2023-09-23" @default.
- W4379924449 title "Hermitian structures on six-dimensional almost nilpotent solvmanifolds" @default.
- W4379924449 doi "https://doi.org/10.48550/arxiv.2306.03485" @default.
- W4379924449 hasPublicationYear "2023" @default.
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