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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.12647 |
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| _version_ | 1866910002660245504 |
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| author | Lee, Dongha |
| author_facet | Lee, Dongha |
| contents | We extend the framework of submanifolds in Riemannian geometry to Riemann-Cartan geometry, which addresses connections with torsion. This procedure naturally introduces a 2-form on submanifolds associated with the nontrivial ambient torsion, whose Hodge dual plays the role of an imaginary counterpart to mean curvature for surfaces in a Riemann-Cartan 3-manifold. We observe that this complex-valued geometric quantity interacts with a number of other geometric concepts including the Hopf differential and the Gauss map, which generalizes classical minimal surface theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complex-valued extension of mean curvature for surfaces in Riemann-Cartan geometry Lee, Dongha Differential Geometry 53A10, 53C05 We extend the framework of submanifolds in Riemannian geometry to Riemann-Cartan geometry, which addresses connections with torsion. This procedure naturally introduces a 2-form on submanifolds associated with the nontrivial ambient torsion, whose Hodge dual plays the role of an imaginary counterpart to mean curvature for surfaces in a Riemann-Cartan 3-manifold. We observe that this complex-valued geometric quantity interacts with a number of other geometric concepts including the Hopf differential and the Gauss map, which generalizes classical minimal surface theory. |
| title | Complex-valued extension of mean curvature for surfaces in Riemann-Cartan geometry |
| topic | Differential Geometry 53A10, 53C05 |
| url | https://arxiv.org/abs/2502.12647 |