## 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*(to appear).

## Additional Information

- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**234**(1977), 253-278 - MSC: Primary 53C05; Secondary 53C15
- DOI: https://doi.org/10.1090/S0002-9947-1977-0500673-0
- MathSciNet review: 0500673