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arXiv · 1908.08832

Harmonic metallic structures

Adara M. Blaga·Antonella Nannicini
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Abstract

The concept of harmonic metallic structure on a metallic pseudo-Riemannian manifold is introduced. In the case of compact manifolds we prove that harmonicity of a metallic structure $J$, with $J^2=pJ+qI$ and $p^2+4q\neq 0$, is equivalent to $dJ=0$. Conditions for a harmonic metallic structure to be preserved by harmonic maps are also given. Moreover, we consider harmonic metallic structures on the generalized tangent bundle, provide a Weitzenb\"{o}ck formula for the dual metallic structure and express the Hodge-Laplace operator on $TM \oplus T^*M$.

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Adara M. Blaga, Antonella Nannicini. 2019-08-23. Harmonic metallic structures. https://arxiv.org/abs/1908.08832

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