Riemannian manifold - Revision history

Vipul: 3 revisions

2008-05-18T20:07:26Z

3 revisions

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Vipul: /* Weaker structures */

2007-08-31T10:58:31Z

Weaker structures

← Older revision		Revision as of 10:58, 31 August 2007
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	* [[Pseudo-Riemannian manifold]]		* [[Pseudo-Riemannian manifold]]
			* [[Metric space]] {{further\|[[Riemannian manifold is metric space]]}}

Vipul at 10:41, 8 March 2007

2007-03-08T10:41:15Z

← Older revision		Revision as of 10:41, 8 March 2007
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	# A [[differential manifold]] <math>M</math>		# A [[differential manifold]] <math>M</math>
	# A [[Riemannian metric]] <math>g</math> on <math>M</math>, viz a smooth association of a positive definite symmetric bilinear form <math>g_p</math> for the tangent space <math>T_p(M)</math>.		# A [[Riemannian metric]] <math>g</math> on <math>M</math>, viz a smooth association of a positive definite symmetric bilinear form <math>g_p</math> for the tangent space <math>T_p(M)</math>.

			==Relation with other structures==

			===Stronger structures===

			* [[Oriented Riemannian manifold]]

			===Weaker structures===

			* [[Pseudo-Riemannian manifold]]

Vipul at 08:32, 8 March 2007

2007-03-08T08:32:31Z

New page

{{structuregroup|[[orthogonal group]]}}

==Definition==

A '''Riemannian manifold''' is the following data:

# A [[differential manifold]] <math>M</math>
# A [[Riemannian metric]] <math>g</math> on <math>M</math>, viz a smooth association of a positive definite symmetric bilinear form <math>g_p</math> for the tangent space <math>T_p(M)</math>.