1111: C∞ (p, q)-Tensors Field over C∞ Manifold with Boundary

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definition of $C^{\mathrm{\infty }}$ (p, q)-tensors field over $C^{\mathrm{\infty }}$ manifold with boundary

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Topics

About: $C^{\mathrm{\infty }}$ manifold

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description

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Starting Context

• The reader knows a definition of $C^{\mathrm{\infty }}$ (p, q)-tensors bundle over $C^{\mathrm{\infty }}$ manifold with boundary.
• The reader knows a definition of section of continuous surjection.

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Target Context

• The reader will have a definition of $C^{\mathrm{\infty }}$ (p, q)-tensors field over $C^{\mathrm{\infty }}$ manifold with boundary.

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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.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$M$: $\in \{\text{ the }{C}^{\mathrm{\infty }}\text{ manifolds with boundary }\}$
$p$: $\in \mathbb{N}$
$q$: $\in \mathbb{N}$
$(T_q^p(TM),M,\pi )$: $=\text{ the }(p,q)\text{ -tensors bundle over }M$
$\ast f$: $:M\to T_q^p(TM)$, $\in \{\text{ the sections of }\pi \}$
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Conditions:
$f\in \{\text{ the }{C}^{\mathrm{\infty }}\text{ maps }\}$
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References

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