Analyzing the Geometry of Immersions of Co-Dimension One via Shape Operator Dynamics
Differential Geometry
2026-05-08 v4
Abstract
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.
Cite
@article{arxiv.2507.12068,
title = {Analyzing the Geometry of Immersions of Co-Dimension One via Shape Operator Dynamics},
author = {Mohammad Javad Habibi Vosta Kolaei},
journal= {arXiv preprint arXiv:2507.12068},
year = {2026}
}
Comments
The definition of the biharmonic tension field is not working in this case. Also I have been known by my colleagues that the introduced flow is not well-studied enough to being used. By all above, I have decided to withdrawn this manuscript and reconsider the issue to avoid any further misunderstanding