Surfaces on Oeljeklaus-Toma Manifolds

2013/06/11 by Sima Verbitsky, Verbitsky, Sima
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1306.2456

openalex publication_date 2013/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Oeljeklaus-Toma manifolds are complex non-Kähler manifolds constructed by Oeljeklaus and Toma from certain number fields. These manifolds generalize Inoue surfaces of type S_m. In this work it is shown that Oeljeklaus-Toma manifolds could not contain any compact complex submanifolds of dimension 2 (surfaces) except Inoue surfaces.

Citations

• On compact complex surfaces of Kähler rank one

Related

• Curves on Oeljeklaus-Toma Manifolds
• Several complex structures on the Oeljeklaus-Toma manifolds
• On generalized Inoue manifolds
• On a generalization of Inoue and Oeljeklaus-Toma manifolds
• Special Hermitian metrics on Oeljeklaus-Toma manifolds