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Parallel Codazzi tensors with submanifold applications

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  • Anthony Gruber

Abstract

A decomposition theorem is established for a class of closed Riemannian submanifolds immersed in a space form of the 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.

Suggested Citation

  • Anthony Gruber, 2023. "Parallel Codazzi tensors with submanifold applications," Mathematische Nachrichten, Wiley Blackwell, vol. 296(9), pages 4032-4042, September.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:9:p:4032-4042
    DOI: 10.1002/mana.202100060
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