Bernstein Theorems for Calibrated Submanifolds in $\mathbb{R}^7$ and $\mathbb{R}^8$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915207973961728 |
|---|---|
| author | Lien, Chun-Kai Tsai, Chung-Jun |
| author_facet | Lien, Chun-Kai Tsai, Chung-Jun |
| contents | This paper explores the Bernstein problem of smooth maps $f:\mathbb{R}^4 \to \mathbb{R}^3$ whose graphs form coassociative submanifolds in $\mathbb{R}^7$. We establish a condition, expressed in terms of the second elementary symmetric polynomial of the map's slope, that ensures $f$ is affine. A corresponding result is also established for Cayley submanifolds in $\mathbb{R}^8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16898 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bernstein Theorems for Calibrated Submanifolds in $\mathbb{R}^7$ and $\mathbb{R}^8$ Lien, Chun-Kai Tsai, Chung-Jun Differential Geometry Primary 53C38, Secondary 53A10, 49Q05, 35J60 This paper explores the Bernstein problem of smooth maps $f:\mathbb{R}^4 \to \mathbb{R}^3$ whose graphs form coassociative submanifolds in $\mathbb{R}^7$. We establish a condition, expressed in terms of the second elementary symmetric polynomial of the map's slope, that ensures $f$ is affine. A corresponding result is also established for Cayley submanifolds in $\mathbb{R}^8$. |
| title | Bernstein Theorems for Calibrated Submanifolds in $\mathbb{R}^7$ and $\mathbb{R}^8$ |
| topic | Differential Geometry Primary 53C38, Secondary 53A10, 49Q05, 35J60 |
| url | https://arxiv.org/abs/2503.16898 |