This research analyzes changes in shape operator dynamics in Riemannian manifolds, suggesting new connections to bi-harmonic maps.
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) studied this question.
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