Abstract
If E → X is a vector bundle, then it is of considerable interest to investigate the special operation derived from the functor “multilinear alternating forms.” Applying it to the tangent bundle, we call the sections of our new bundle differential forms. One can define formally certain relations between functions, vector fields, and differential forms which lie at the foundations of differential and Riemannian geometry. We shall give the basic system surrounding such forms. In order to have at least one application, we discuss the fundamental 2-form, and in the next chapter connect it with Riemannian metrics in order to construct canonically the spray associated with such a metric.
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© 1999 Springer Science+Business Media New York
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Lang, S. (1999). Operations on Vector Fields and Differential Forms. In: Fundamentals of Differential Geometry. Graduate Texts in Mathematics, vol 191. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0541-8_5
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DOI: https://doi.org/10.1007/978-1-4612-0541-8_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6810-9
Online ISBN: 978-1-4612-0541-8
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