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 R n (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.
KeywordsOpen Subset Tangent Space Tangent Vector Open Neighborhood Tubular Neighborhood
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