Analyzing the Geometry of Immersions of Co-Dimension One via Shape Operator Dynamics
Mohammad Javad Habibi Vosta Kolaei · arXiv (Cornell University) · 2025
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.