Abstract
This chapter forms the backbone of this book, and it is the one with the greatest number of exercises. We first define and give examples of submanifolds of Rn (section 2.1), the right concrete objects for the study of differential geometry. Next we define parametrizations of submanifolds; coordinate changes from one parametrization to another are the essential ingredients in the definition of abstract manifolds (section 2.2), which are the right objects for the study of abstract (and sometimes even concrete) differential geometry.
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© 1988 Springer Science+Business Media New York
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Berger, M., Gostiaux, B. (1988). Differentiable Manifolds. In: Differential Geometry: Manifolds, Curves, and Surfaces. Graduate Texts in Mathematics, vol 115. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1033-7_3
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DOI: https://doi.org/10.1007/978-1-4612-1033-7_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6992-2
Online ISBN: 978-1-4612-1033-7
eBook Packages: Springer Book Archive