Harmonic metallic structures

2019/08/23 by Blaga, Adara M., Nannicini, Antonella
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.08832

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 J²=pJ+qI and p²+4q≠ 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 Weitzenböck formula for the dual metallic structure and express the Hodge-Laplace operator on TM ⊕ T^*M.

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