Generalized complex Stein manifold
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912018686017536 |
|---|---|
| author | Pal, Debjit |
| author_facet | Pal, Debjit |
| contents | 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 $L^2$ 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 $\mathbb{R}^{2n-2k} \times \mathbb{C}^{2k+1}$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized complex Stein manifold Pal, Debjit Differential Geometry Complex Variables Functional Analysis Primary: 53D18, 32Q28, 32C35, 32H02. Secondary: 32Q40, 46E35, 32U10 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 $L^2$ 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 $\mathbb{R}^{2n-2k} \times \mathbb{C}^{2k+1}$, 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. |
| title | Generalized complex Stein manifold |
| topic | Differential Geometry Complex Variables Functional Analysis Primary: 53D18, 32Q28, 32C35, 32H02. Secondary: 32Q40, 46E35, 32U10 |
| url | https://arxiv.org/abs/2409.01912 |