Parabolic and Hyperbolic Inoue Surfaces
Parabolic and hyperbolic Inoue surfaces are Kodaira class VII surfaces defined by Iku Nakamura in 1984. They are not solvmanifolds. These surfaces have positive second Betti number. They have spherical shells, and can be deformed into a blown-up Hopf surface.
Parabolic Inoue surfaces are also known as half-Inoue surfaces. These surfaces can be defined as class VII0 (that is, class VII and minimal) surfaces with an elliptic curve and a cycle of rational curves.
Hyperbolic Inoue surfaces are class VII0 surfaces with two cycles of rational curves.
Read more about this topic: Inoue Surface
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