We classify and investigate locally conformally K"ahler structures on four-dimensional solvable Lie algebras up to linear equivalence. As an application we can produce many examples in higher dimension, here including lcK structures on Oeljeklaus-Toma manifolds, and we also give a geometric interpretation of some of the $4$-dimensional structures in our classification.
Locally conformally K"ahler structures on four-dimensional solvable Lie algebras / Daniele Angella; Marcos Origlia. - In: COMPLEX MANIFOLDS. - ISSN 2300-7443. - ELETTRONICO. - 7:(2020), pp. 1-35. [10.1515/coma-2020-0001]
Locally conformally K"ahler structures on four-dimensional solvable Lie algebras
Daniele Angella
;Marcos Origlia
2020
Abstract
We classify and investigate locally conformally K"ahler structures on four-dimensional solvable Lie algebras up to linear equivalence. As an application we can produce many examples in higher dimension, here including lcK structures on Oeljeklaus-Toma manifolds, and we also give a geometric interpretation of some of the $4$-dimensional structures in our classification.
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