Harmonic metallic structures

zbMATH Open1471.53024arXiv1908.08832MaRDI QIDQ4992975

Adara M. Blaga, Antonella Nannicini

Publication date: 14 June 2021

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 $p^2+4qeq0$, 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 $TMoplus{T}^{*}M$.

Full work available at URL: https://arxiv.org/abs/1908.08832

zbMATH Keywords

harmonic mapsharmonic structuresmetallic pseudo-Riemannian structures

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Calculus on manifolds; nonlinear operators (58C99)

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