On curvature tensors of Norden and metallic pseudo-Riemannian manifolds
We study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds. We introduce the notion of J-sectional and J-bisectional curvature of a metallic pseudo-Riemannian manifold (M, J, g) and study their properties.We prove that under certain assumptions,...
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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2019
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/515747c623b9462680efa7cd26b0f576 |
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| Sumario: | We study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds. We introduce the notion of J-sectional and J-bisectional curvature of a metallic pseudo-Riemannian manifold (M, J, g) and study their properties.We prove that under certain assumptions, if the manifold is locally metallic, then the Riemann curvature tensor vanishes. Using a Norden structure (J, g) on M, we consider a family of metallic pseudo-Riemannian structures {Ja,b}a,b∈ℝ and show that for a ≠ 0, the J-sectional and J-bisectional curvatures of M coincide with the Ja,b-sectional and Ja,b-bisectional curvatures, respectively. We also give examples of Norden and metallic structures on ℝ2n. |
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