Structure of symmetric tensors of type and tensors of type on the tangent bundle
Authors:
Kam Ping Mok, E. M. Patterson and Yung Chow Wong
Journal:
Trans. Amer. Math. Soc. 234 (1977), 253278
MSC:
Primary 53C05; Secondary 53C15
MathSciNet review:
0500673
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Abstract: The concepts of Mtensor and Mconnection 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 Mconnection. They involve extending known results on TM using tensors on M to cases in which these tensors are replaced by Mtensors. 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197705006730
PII:
S 00029947(1977)05006730
Keywords:
Tangent bundle,
Sasaki metric,
Mtensor,
Mconnection,
adapted frame,
(pseudo) Riemannian metric,
almost product structure,
almost complex structure
Article copyright:
© Copyright 1977
American Mathematical Society
