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- Thread starter yuiop
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For example: the 3-sphere S

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quasar987

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...and Riemannian geometry!You should read about manifolds.

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lavinia

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If you have a 3d coordinate system that is described by lines with known lengths and angles - e.g. a geodesic coordinate system - then you do not need to embed that manifold into 4d or higher in order to see its geometry. This is the geometry you would observe by measurement on the manifold itself rather than the geometry you get by looking down on it from the outside.

There is a difference between the intrinsic geometry and the embedded geometry. Intrinsic geometry does not tell you how the manifold bends and curves in space whereas extrinsic does. However the two geometries are intimately linked. For instance, the Gauss curvature of a surface - which is intrinsic - can be determined by the way the unit normal in 3 space changes direction as you move it around on the surface.

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