论文标题
带有子手机应用的平行CoDazzi张量
Parallel Codazzi tensors with submanifold applications
论文作者
论文摘要
为一类浸入恒定截面曲率的空间形式的封闭的Riemannian Submanifolds建立了分解定理。特别是，如果$ m $具有非负分段曲率，并承认具有“平行平均曲率”的codazzi张量，则$ m $是该张量频谱确定的不可减免因子的直接乘积。当$ M $仅连接并概括为具有平均平均值曲率向量的沉浸式亚体而闻名的$ M $时，该分解是全局的。
A decomposition theorem is established for a class of closed Riemannian submanifolds immersed in a space form of constant sectional curvature. In particular, it is shown that if $M$ has nonnegative sectional curvature and admits a Codazzi tensor with "parallel mean curvature", then $M$ is locally isometric to a direct product of irreducible factors determined by the spectrum of that tensor. This decomposition is global when $M$ is simply connected, and generalizes what is known for immersed submanifolds with parallel mean curvature vector.
