ANNALES POLONICI MATHEMATICI 99.2 (2010) On para-Nordenian structures by Arif A. Salimov (Erzurum and Baku) and Filiz Agca (Trabzon) Abstract. The aim of this paper is to investigate para-Nordenian properties of the Sasakian metrics in the cotangent bundle. 1. Introduction. Let (M n ,g) be an n-dimensional Riemannian mani- fold, T * M n its cotangent bundle and π the natural projection T * M n → M n . A system of local coordinates (U, x i ), i =1,...,n on M n induces on T * M n a system of local coordinates (π -1 (U ),x i ,x ¯ı = p i ), ¯ı := n + i (¯ı =1,..., 2n), where x ¯ı = p i are the components of the covector p in each cotangent space T * x M n , x ∈ U , with respect to the natural coframe {dx i }, i =1,...,n. We denote by = r s (M n ) (resp. = r s (T * M n )) the module over F (M n ) (resp. F (T * M n )) of C ∞ tensor fields of type (r, s), where F (M n ) (resp. F (T * M n )) is the ring of real-valued C ∞ functions on M n (resp. T * M n ). Let X = X i ∂ ∂x i and ω = ω i dx i be the local expressions in U ⊂ M n of a vector and a covector (1-form) field X ∈= 1 0 (M n ) and ω ∈= 0 1 (M n ), respectively. Then the complete and horizontal lifts C X, H X ∈= 1 0 (T * M n ) of X ∈= 1 0 (M n ) and the vertical lift V ω ∈= 1 0 (T * M n ) of ω ∈= 0 1 (M n ) are given, respectively, by C X = X i ∂ ∂x i - X i p h ∂ i X h ∂ ∂x ¯ı , (1.1) H X = X i ∂ ∂x i + X i p h Γ h ij X j ∂ ∂x ¯ı , (1.2) V ω = X i ω i ∂ ∂x ¯ı (1.3) with respect to the natural frame  ∂ ∂x i , ∂ ∂x ¯ı  , where Γ h ij are the components of the Levi-Civita connection ∇ g on M n (see [11] for more details). 2010 Mathematics Subject Classification : Primary 53C07; Secondary 53C15. Key words and phrases : Sasakian metric, cotangent bundle, vertical and horizontal lift, para-Nordenian metric. DOI: 10.4064/ap99-2-6 [193] c  Instytut Matematyczny PAN, 2010