On curvature tensors of Norden and metallic pseudo-Riemannian manifolds
Keyword(s):
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.
2016 ◽
Vol 25
(10)
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pp. 1650055
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1984 ◽
Vol 23
(10)
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pp. 1001-1008
2021 ◽
2018 ◽
1985 ◽
Vol 97
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pp. 173-192
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Keyword(s):
1988 ◽
Vol 5
(5)
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pp. 695-705
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