Affiliation:
1. Department of Mathematics, West University of Timişoara, Bld. V. Pârvan nr. 4, 300223, Timişoara, România
2. Department of Mathematics and Informatics “U. Dini”, University of Florence, Viale Morgagni, 67/a, 50134, Firenze, Italy
Abstract
AbstractWe 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.
Reference12 articles.
1. On Geometry of Manifolds with Some Tensor Structures and Metrics of Type arXiv math;Manev
2. Anti manifolds no;Borowiec;Geom,2000
3. Nearly manifolds;Gray,1970
4. On the curvature of manifolds no;Sluka;Geom Phys,2005
5. Generalized metallic pseudo Riemannian structures arXiv math;Blaga,1811
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