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math.DG2023
Harmonic curvature in dimension four
Andrzej Derdzinski
We provide a step towards classifying Riemannian four-manifolds in which the curvature tensor has zero divergence, or -- equivalently -- the Ricci tensor Ric satisfies the Codazzi…
math.DG2023
Compact flat manifolds and reducibility
Andrzej Derdzinski, Paolo Piccione
Hiss and Szczepański proved in 1991 that the holonomy group of any compact flat Riemannian manifold, of dimension at least two, acts reducibly on the rational span of the Euclidean…