On compact Riemannian manifolds, a metallic structure J with J² = pJ + qI is harmonic exactly when its exterior derivative dJ vanishes, provided p² + 4q ≠ 0.
On the geometry of metallic pseudo-Riemannian structures
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abstract
We generalize the notion of metallic structure in the pseudo-Riemannian setting, define the metallic Norden structure and study its integrability. We consider metallic maps between metallic manifolds and give conditions under which they are constant. We also construct a metallic natural connection recovering as particular case the Ganchev and Mihova connection, which we extend to a metallic natural connection on the generalized tangent bundle. Moreover, we construct metallic pseudo-Riemannian structures on the tangent and cotangent bundles.
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math.DG 1years
2019 1verdicts
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Harmonic metallic structures
On compact Riemannian manifolds, a metallic structure J with J² = pJ + qI is harmonic exactly when its exterior derivative dJ vanishes, provided p² + 4q ≠ 0.