Structure of symmetric tensors of type (0,2) and tensors of type (1,1) on the tangent bundle

Mok, Kam Ping; Patterson, E. M.; Wong, Yung Chow

doi:10.1090/S0002-9947-1977-0500673-0

Structure of symmetric tensors of type $(0, 2)$ and tensors of type $(1, 1)$ on the tangent bundle
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by Kam Ping Mok, E. M. Patterson and Yung Chow Wong PDF

Trans. Amer. Math. Soc. 234 (1977), 253-278 Request permission

Abstract:

The concepts of M-tensor and M-connection on the tangent bundle TM of a smooth manifold M are used in a study of symmetric tensors of type (0, 2) and tensors of type (1, 1) on TM. The constructions make use of certain local frames adapted to an M-connection. They involve extending known results on TM using tensors on M to cases in which these tensors are replaced by M-tensors. Particular attention is devoted to (pseudo-) Riemannian metrics on TM, notably those for which the vertical distribution on TM is null or nonnull, and to the construction of almost product and almost complex structures on TM.

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Structure of tensors on the cotangent bundle

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