definition of global differential of \(C^\infty\) map between \(C^\infty\) manifolds with boundary
Topics
About: \(C^\infty\) manifold
The table of contents of this article
Starting Context
Target Context
- The reader will have a definition of global differential of \(C^\infty\) map between \(C^\infty\) manifolds with boundary.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( M_1\): \(\in \{\text{ the } C^\infty \text{ manifolds with boundary }\}\)
\( M_2\): \(\in \{\text{ the } C^\infty \text{ manifolds with boundary }\}\)
\( f\): \(: M_1 \to M_2\), \(\in \{\text{ the } C^\infty \text{ maps }\}\)
\( (T M_1, M_1, \pi_1)\): \(= \text{ the tangent vectors bundle }\)
\( (T M_2, M_2, \pi_2)\): \(= \text{ the tangent vectors bundle }\)
\(*d f\): \(: T M_1 \to T M_2, v \mapsto d f_{\pi_1 (v)} v\)
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Conditions:
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