Parallel Codazzi tensors with submanifold applications

Anthony Gruber

Mathematische Nachrichten, 2023, vol. 296, issue 9, 4032-4042

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.

Date: 2023
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