Some properties of Sasakian metrics in cotangent bundles
The authors investigate curvature properties of the Sasakian metrics in the cotangent bundle. Let \((M_{n}, g)\) be an \(n\)-dimensional differentiable Riemannian manifold of class \(\mathcal{C}^{\infty}\) and \({}^{C}T (M_{n})\) be its cotangent bundle. When \({}^{C}T (M_{n})\) is endowed with a Sasakian metric \({}^{S}g\), they prove that \({}^{C}T (M_{n})\) is flat if and only if \(M_{n}\) is flat. They also obtain some characterizing theorems on \(({}^{C}T (M_{n}), {}^{S}g)\).
scientific article; zbMATH DE number 5911439