Inoue surface

In complex geometry, a part of mathematics, the term Inoue surface denotes several complex surfaces of Kodaira class VII. They are named after Masahisa Inoue, who gave the first non-trivial examples of Kodaira class VII surfaces in 1974.

The Inoue surfaces are not Kähler manifolds.

Inoue introduced three families of surfaces, S⁰, S⁺ and S⁻, which are compact quotients of ${\displaystyle {\mathbb {C}}\times H}$ (a product of a complex plane by a half-plane). These Inoue surfaces are solvmanifolds. They are obtained as quotients of ${\displaystyle {\mathbb {C}}\times H}$ by a solvable discrete group which acts holomorphically on ${\displaystyle {\mathbb {C}}\times H}$.

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