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math.DG2026
On the Bach tensor and quadratic curvature functionals
Letizia Branca, Davide Dameno
We study the critical points of a quadratic functional depending on the gradient of the Bach tensor on Riemannian four-manifolds, which generalize the Bach-flat condition. We show…
math.DG2026
Conformal Kähler rigidity of Einstein four-manifolds
Giovanni Catino, Davide Dameno
For a compact, connected, oriented Einstein four-manifold, we prove that, if the largest eigenvalue of the self-dual Weyl curvature is everywhere simple, then, after at worst…
math.DG2026
Topological and rigidity results for four-dimensional hypersurfaces in space forms
Davide Dameno, Aaron J. Tyrrell
Exploiting the special features of four-dimensional Riemannian geometry, we derive topological and rigidity results for hypersurfaces immersed in space forms of dimension 5. First,…