In this chapter we introduce the concept of a regular submanifold of a manifold, a subset that is locally defined by the vanishing of some of the coordinate functions. Using the inverse function theorem, we derive a criterion, called the regular level set theorem, that can often be used to show that a level set of a C∞ map of manifolds is a regular submanifold and therefore a manifold.
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© 2008 Springer Science+Business Media, LLC
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(2008). Submanifolds. In: An Introduction to Manifolds. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-0-387-48101-2_9
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DOI: https://doi.org/10.1007/978-0-387-48101-2_9
Publisher Name: Springer, New York, NY
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