In this paper, we introduce a new method to obtain a metallic semi-Riemannian structure $ (\Psi, \widetilde{g}) $ from the given almost paracontact metric structure $ (\varphi, \xi, \eta, g) $ on a smooth manifold $ M^{2n+1} $, and give the relations between these structures via Levi-Civita connections of $ g $ and $ \widetilde{g} $. After, we discuss these relations for para-Kenmotsu and para-Sasakian structures and state the properties of obtained metallic semi-Riemannian structure. Furthermore, we show that metallic structures obtained from para-Kenmotsu and para-Sasakian structures are integrable and non-integrable, respectively. Also, we study the curvature properties of the obtained metallic structure and give explicit examples for the results of the study.
Citation: Mehmet Solgun, Yasemin Karababa. Constructing a metallic semi-Riemannian manifold from an almost paracontact metric manifold[J]. AIMS Mathematics, 2025, 10(10): 23639-23651. doi: 10.3934/math.20251050
In this paper, we introduce a new method to obtain a metallic semi-Riemannian structure $ (\Psi, \widetilde{g}) $ from the given almost paracontact metric structure $ (\varphi, \xi, \eta, g) $ on a smooth manifold $ M^{2n+1} $, and give the relations between these structures via Levi-Civita connections of $ g $ and $ \widetilde{g} $. After, we discuss these relations for para-Kenmotsu and para-Sasakian structures and state the properties of obtained metallic semi-Riemannian structure. Furthermore, we show that metallic structures obtained from para-Kenmotsu and para-Sasakian structures are integrable and non-integrable, respectively. Also, we study the curvature properties of the obtained metallic structure and give explicit examples for the results of the study.
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Mehmet Solgun, Yasemin Karababa. Constructing a metallic semi-Riemannian manifold from an almost paracontact metric manifold[J]. AIMS Mathematics, 2025, 10(10): 23639-23651. doi: 10.3934/math.20251050
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