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:	Blaga Adara M., Nannicini Antonella
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2019
Materias:	norden manifolds metallic pseudo-riemannian structures j-sectional curvature j-bisectional curvature 53c15 53c25 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/515747c623b9462680efa7cd26b0f576
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spelling	oai:doaj.org-article:515747c623b9462680efa7cd26b0f5762021-12-02T17:14:47ZOn curvature tensors of Norden and metallic pseudo-Riemannian manifolds2300-744310.1515/coma-2019-0008https://doaj.org/article/515747c623b9462680efa7cd26b0f5762019-01-01T00:00:00Zhttps://doi.org/10.1515/coma-2019-0008https://doaj.org/toc/2300-7443We 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.Blaga Adara M.Nannicini AntonellaDe Gruyterarticlenorden manifoldsmetallic pseudo-riemannian structuresj-sectional curvaturej-bisectional curvature53c1553c25MathematicsQA1-939ENComplex Manifolds, Vol 6, Iss 1, Pp 150-159 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	norden manifolds metallic pseudo-riemannian structures j-sectional curvature j-bisectional curvature 53c15 53c25 Mathematics QA1-939
spellingShingle	norden manifolds metallic pseudo-riemannian structures j-sectional curvature j-bisectional curvature 53c15 53c25 Mathematics QA1-939 Blaga Adara M. Nannicini Antonella On curvature tensors of Norden and metallic pseudo-Riemannian manifolds
description	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.
format	article
author	Blaga Adara M. Nannicini Antonella
author_facet	Blaga Adara M. Nannicini Antonella
author_sort	Blaga Adara M.
title	On curvature tensors of Norden and metallic pseudo-Riemannian manifolds
title_short	On curvature tensors of Norden and metallic pseudo-Riemannian manifolds
title_full	On curvature tensors of Norden and metallic pseudo-Riemannian manifolds
title_fullStr	On curvature tensors of Norden and metallic pseudo-Riemannian manifolds
title_full_unstemmed	On curvature tensors of Norden and metallic pseudo-Riemannian manifolds
title_sort	on curvature tensors of norden and metallic pseudo-riemannian manifolds
publisher	De Gruyter
publishDate	2019
url	https://doaj.org/article/515747c623b9462680efa7cd26b0f576
work_keys_str_mv	AT blagaadaram oncurvaturetensorsofnordenandmetallicpseudoriemannianmanifolds AT nanniciniantonella oncurvaturetensorsofnordenandmetallicpseudoriemannianmanifolds
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On curvature tensors of Norden and metallic pseudo-Riemannian manifolds

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