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Title: Coordinate Basis
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Series: Manifolds
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YouTube-Title: Manifolds 22 | Coordinate Basis
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Bright video: https://youtu.be/BjU8-n4ixqo
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Dark video: https://youtu.be/MS-SfgKYDd0
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Ad-free video: Watch Vimeo video
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: mf22_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $M$ be a smooth manifold of dimension $n$. What is the dimension of $T_p(M)$?
A1: $n$
A2: 0
A3: $n^2$
A4: $n-1$
Q2: Let $M$ be a smooth manifold of dimension $n$. What is a basis of $T_p(M)$?
A1: $(\varphi_{\ast} (e_1), \ldots, \varphi_{\ast} (e_n) )$
A2: $(e_1, \ldots, e_n)$
A3: $(h (e_1), \ldots, h(e_n))$
Q3: Let $M$ be a smooth submanifold in $\mathbb{R}^n$ of dimension $k$ . What is a basis of $T^{\textrm{sub}}_p(M)$?
A1: $(\frac{\partial \varphi}{\partial x_1}(\tilde{p}) \ldots, \frac{\partial \varphi}{\partial x_n}(\tilde{p}))$
A2: $(e_1, \ldots, e_n)$
A3: $(h (e_1), \ldots, h(e_n))$
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Last update: 2024-10
