Kähler submanifolds in Iwasawa manifolds

2017/10/05 by Vasily Rogov, Rogov, Vasily
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1710.02180

18 pages

openalex publication_date 2017/10/05 · arxiv created 2018/04/06 · arxiv updated 2018/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Iwasawa manifold is a compact complex homogeneous manifold isomorphic to a quotient of the group of complex unipotent 3 × 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.

Related

• Compact Kähler manifolds with elliptic homotopy type
• Holomorphic symmetric differentials and parallelizable compact complex manifolds
• Complex structures on the Iwasawa manifold
• Solvable models for Kodaira surfaces
• Algebraic approximations of compact Kähler threefolds