Parallel Codazzi tensors with submanifold applications

Anthony Gruber

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arXiv · 2004.03103

Parallel Codazzi tensors with submanifold applications

Anthony Gruber

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Abstract

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.

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Anthony Gruber. 2020-04-07. Parallel Codazzi tensors with submanifold applications. https://arxiv.org/abs/2004.03103

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