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 A new class of Riemannian metrics on tangent bundle of a Riemannian manifold Commun. Korean Math. Soc.Published online August 28, 2020 Amir Baghban and Saeed Hashemi Sababe Facultu of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran, Department of Mathematical and Statistical Sciences, University of Alberta Abstract : The class of isotropic almost complex structures, $J_{\delta , \sigma}$, define a class of Riemannian metrics, $g_{\delta , \sigma}$, on the tangent bundle of a Riemannian manifold which are a generalization of the Sasaki metric. This paper characterizes the metrics $g_{\delta , 0}$ using the geometry of tangent bundle. As a by-product, some integrability results will be reported for $J_{\delta , \sigma}$. Keywords : Einstein manifold, isotropic almost complex structure, integrability, space form, tangent bundle MSC numbers : 53C25, 53C15 Full-Text :