Solvmanifolds and Generalized Kähler Structures


Abstract


We review generalized complex geometry in relation with solvmanifolds and we describe the construction in [17] of a generalized Kähler structure on a 6-dimensional solvmanifold. The compact manifold is the total space of a 𝕋2-bundle over an Inoue surface and does not admit any Kähler structure.

DOI Code: 10.1285/i15900932v28n1supplp169

Keywords: generalized complex structure; generalized Kähler structure; solvmanifold; Hermitian metric; torsion

Classification: 53C30; 53C35; 53C50

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