Analyzing the Geometry of Immersions of Co-Dimension One via Shape Operator Dynamics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917465582206976 |
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| author | Kolaei, Mohammad Javad Habibi Vosta |
| author_facet | Kolaei, Mohammad Javad Habibi Vosta |
| contents | We study the extrinsic geometry of isometric immersions into Riemannian manifolds of co-dimension one via a fourth-order geometric evolution of the shape operator. Motivated by bi-harmonic map theory and generalized Chen's conjecture, we introduce a moduli flow, a tensorial gradient flow that decreases a natural energy measuring curvature variation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analyzing the Geometry of Immersions of Co-Dimension One via Shape Operator Dynamics Kolaei, Mohammad Javad Habibi Vosta Differential Geometry 53C42, 35K55, 58J35 We study the extrinsic geometry of isometric immersions into Riemannian manifolds of co-dimension one via a fourth-order geometric evolution of the shape operator. Motivated by bi-harmonic map theory and generalized Chen's conjecture, we introduce a moduli flow, a tensorial gradient flow that decreases a natural energy measuring curvature variation. |
| title | Analyzing the Geometry of Immersions of Co-Dimension One via Shape Operator Dynamics |
| topic | Differential Geometry 53C42, 35K55, 58J35 |
| url | https://arxiv.org/abs/2507.12068 |