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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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

Authors: Kam Ping Mok, E. M. Patterson and Yung Chow Wong
Journal: Trans. Amer. Math. Soc. 234 (1977), 253-278
MSC: Primary 53C05; Secondary 53C15
MathSciNet review: 0500673
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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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Keywords: Tangent bundle, Sasaki metric, <I>M</I>-tensor, <I>M</I>-connection, adapted frame, (pseudo-) Riemannian metric, almost product structure, almost complex structure
Article copyright: © Copyright 1977 American Mathematical Society