2020/04/07 by Gruber, Anthony
#53C25 #53C40 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2004.03103
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.