Harmonic metallic structures
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
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| _version_ | 1866908474029375488 |
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| author | Blaga, Adara M. Nannicini, Antonella |
| author_facet | Blaga, Adara M. Nannicini, Antonella |
| contents | 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 Weitzenböck formula for the dual metallic structure and express the Hodge-Laplace operator on $TM \oplus T^*M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_08832 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Harmonic metallic structures Blaga, Adara M. Nannicini, Antonella Differential Geometry 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 Weitzenböck formula for the dual metallic structure and express the Hodge-Laplace operator on $TM \oplus T^*M$. |
| title | Harmonic metallic structures |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1908.08832 |