math214:02-12
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math214:02-12 [2020/02/11 22:37] pzhou created |
math214:02-12 [2020/02/11 22:50] (current) pzhou [Tubular Neighborhood Theorem] |
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| $$ V = \{(x,v) \in NM : |v| < \delta(x) \}$$ | $$ V = \{(x,v) \in NM : |v| < \delta(x) \}$$ | ||
| for some positive continuous function $\delta: M \to \R$. | for some positive continuous function $\delta: M \to \R$. | ||
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| + | See Thm 6.24 for a proof of the existence of a tubular neighborhood. Mainly, one try to construct the ' | ||
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| + | We define a map $r: U \to M$, that is identity map when restrict to $M$, such a map is called a retraction. | ||
| + | $r: = \pi \circ E^{-1}$, where $\pi: NM \to M$ is the projection map. | ||
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math214/02-12.1581489425.txt.gz · Last modified: 2020/02/11 22:37 by pzhou
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