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2007-03-08T10:46:28Z

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{{structuregroup|[[positive-determinant general linear group]]}}

==Definition==

An '''oriented manifold''' comprises the following data:

* A [[differential manifold]] <math>M</math>
* An ''orientation'' on the tangent space at each point of <math>M</math>, in such a way that the orientation varies smoothly with the point.

A differential manifold that can be given the structure of an oriented manifold is termed an [[orientable manifold]].

For a connected orientable manifold, there are only two possible orientations (a given orientation and its negative). Hence, the additional structure of being ''oriented'' is not often clearly distinguished from the manifold property of being ''orientable''.

==Relation with other structures==

===Stronger structures===

* [[Oriented Riemannian manifold]]
* [[Almost symplectic manifold]]
* [[Symplectic manifold]]
* [[Almost complex manifold]]
* [[Complex manifold]]

Oriented manifold - Revision history

Vipul: 1 revision

Vipul at 10:46, 8 March 2007