Abstract
Suppose V is a nonvanishing vector field on a manifold M. The results of Chapter 17 imply that each integral curve of V is an immersion, and that locally the images of the integral curves fit together nicely like parallel lines in Euclidean space. The fundamental theorem on flows tells us that these curves are determined by the knowledge of their tangent vectors.
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© 2003 Springer Science+Business Media New York
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Lee, J.M. (2003). Integral Manifolds and Foliations. In: Introduction to Smooth Manifolds. Graduate Texts in Mathematics, vol 218. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21752-9_19
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DOI: https://doi.org/10.1007/978-0-387-21752-9_19
Publisher Name: Springer, New York, NY
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