标题： 通过形状算子动力学分析余维一浸入的几何结构 显示英文标题

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

摘要： 我们通过形状算子的四阶几何演化来研究浸入到余维一黎曼流形中的等距浸入的外在几何。 受双调和映射理论和广义Chen猜想的启发，我们引入了一个模流，这是一个张量梯度流，它能减少一个衡量曲率变化的自然能量。 显示英文摘要

摘要： 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.