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MR500673 53C05 (53C15)
Mok, Kam Ping; Patterson, E. M.; Wong, Yung Chow Structure of symmetric tensors of type $(0, 2)$ and tensors of type $(1, 1)$ on the tangent bundle. Trans. Amer. Math. Soc. 234 (1977), no. 1, 253–278.
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