Generalized complex Stein manifold

2024/09/03 by Debjit Pal, Pal, Debjit
Mathematics · #32C35 #32H02. Secondary: 32Q40 #32Q28 #32U10 #46E35 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary: 53D18

paper · pdf · doi:10.48550/arxiv.2409.01912

openalex publication_date 2024/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of a generalized complex (GC) Stein manifold and provide complete characterizations in three fundamental aspects. First, we extend Cartan's Theorem A and B within the framework of GC geometry. Next, we define L-plurisubharmonic functions and develop an associated L² theory. This leads to a characterization of GC Stein manifolds using L-plurisubharmonic exhaustion functions. Finally, we establish the existence of a proper GH embedding from any GC Stein manifold into ℝ^2n-2k × ℂ^2k+1, where 2n and k denote the dimension and type of the GC Stein manifold, respectively. This provides a characterization of GC Stein manifolds via GH embeddings. Several examples of GC Stein manifolds are given.

Related

• Pluricomplex Green Functions on Stein Manifolds and Certain Linear Topological Invariants
• Pluricomplex Green functions on manifolds
• On the Theory of Stein Manifolds
• Stein structures: existence and flexibility
• A note on submanifolds and mappings in generalized complex geometry