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In this article, we consider the almost Hermitian structure on $TM$ inducedby a pair of a metric and an affine connection on $M$. We find the conditionsunder which $TM$ admits almost K\"ahler structures, K\"ahler structures andEinstein metrics, respectively. Moreover, we give two examples ofK\"ahler-Einstein structures on $TM$.

Almost Hermitian structures on tangent bundles