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arXiv · 2507.12068

Analyzing the Geometry of Immersions of Co-Dimension One via Shape Operator Dynamics

Mohammad Javad Habibi Vosta Kolaei
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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.

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Mohammad Javad Habibi Vosta Kolaei. 2025-07-16. Analyzing the Geometry of Immersions of Co-Dimension One via Shape Operator Dynamics. https://arxiv.org/abs/2507.12068

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