Kähler submanifolds in Iwasawa manifolds

Abstract

Iwasawa manifold is a compact complex homogeneous manifold isomorphic to a quotient of the group of complex unipotent $3\times 3$ matrices by a cocompact lattice. We prove that any compact complex curve in an Iwasawa manifold is contained in a holomorphic torus. We also prove that any Kähler surface in an Iwasawa manifold is either an abelian surface or a non-projective isotrivial elliptic surface of Kodaira dimension one. In the Appendix we show that any complex torus in an Iwasawa manifold carries complex multiplication.

18 pages

References in corpus (2)

• Geometry of nilmanifolds with left-invariant complex structure and deformations in the large
• Rational curves and special metrics on twistor spaces