Vipul: 2 revisions

2008-05-18T20:09:11Z

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Vipul at 20:57, 5 April 2008

2008-04-05T20:57:50Z

← Older revision		Revision as of 20:57, 5 April 2008
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			{{global analog\|Lie algebra of global derivations}}
	==Definition==		==Definition==

Vipul: New page: ==Definition== ===Definition in terms of the tangent bundle=== Let $M$ be a differential manifold. The '''sheaf of derivations''' of $M$ is defined as the sheaf...

2008-04-03T22:38:07Z

New page: ==Definition== ===Definition in terms of the tangent bundle=== Let <math>M</math> be a differential manifold. The '''sheaf of derivations''' of <math>M</math> is defined as the sheaf...

New page

==Definition==

===Definition in terms of the tangent bundle===

Let <math>M</math> be a [[differential manifold]]. The '''sheaf of derivations''' of <math>M</math> is defined as the sheaf of smooth sections of the tangent bundle of the manifold. In other words:

* For every open subset <math>U</math> of <math>M</math>, the associated object is the vector space of all smooth sections of the tangent bundle on <math>U</math>, i.e. smooth [[vector field]]s on <math>U</math>
* The restriction map is the restriction of a vector field from a larger open subset to a smaller open subset

===Definition in terms of algebraic theory of derivations===

Let <math>M</math> be a [[differential manifold]]. The '''sheaf of derivations''' of <math>M</math> is defined as the algebra-theoretic [[sheaf of derivations]] for the [[sheaf of infinitely differentiable functions]] on <math>M</math>.

Sheaf of derivations of a manifold - Revision history

Vipul: 2 revisions

Vipul at 20:57, 5 April 2008

Vipul: New page: ==Definition== ===Definition in terms of the tangent bundle=== Let M be a differential manifold. The '''sheaf of derivations''' of M is defined as the sheaf...

Vipul: New page: ==Definition== ===Definition in terms of the tangent bundle=== Let $M$ be a differential manifold. The '''sheaf of derivations''' of $M$ is defined as the sheaf...