A Family of Complex Nilmanifolds with in finitely Many Real Homotopy Types

Abstract

We find a one-parameter family of non-isomorphic nilpotent Lie algebras ga, with a > [0,∞), of real dimension eight with (strongly non-nilpotent) complex structures. By restricting a to take rational values, we arrive at the existence of infinitely many real homotopy types of 8-dimensional nilmanifolds admitting a complex structure. Moreover, balanced Hermitian metrics and generalized Gauduchon metrics on such nilmanifolds are constructed.

Keywords

• nilmanifold
• nilpotent lie algebra
• complex structure
• hermitian metric
• homotopy theory
• minimal model
• 55p62
• 17b30
• 53c55