3 problems

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Spherical space form conjecture for manifolds with harmonic curvature
Spherical space form question. Must every closed manifold with harmonic curvature and $(n+\frac{n-2}{n})$ -positive curvature operator of the second kind be diffeomorphic to a spher…
Problemsolvedcurvature-operators harmonic-curvature riemannian-geometryarXiv posted 2 days ago
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The conjecture that homogeneous Riemannian manifolds with harmonic curvature are Ricci-parallel
Homogeneous harmonic-curvature conjecture. Any homogeneous Riemannian manifold $M$ with harmonic curvature is Ricci-parallel:
Conjectureopenharmonic-curvature homogeneous-geometry riemannian-geometryarXiv posted 2 days ago
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The homogeneous harmonic-curvature conjecture
Homogeneous harmonic-curvature conjecture. Any homogeneous Riemannian manifold $M$ with harmonic curvature is Ricci-parallel.
Conjectureopenharmonic-curvature homogeneous-spaces riemannian-geometryarXiv posted 2 days ago

Spherical space form conjecture for manifolds with harmonic curvature