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.References
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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