# Curved space and curvilinear coordinates

• I
hi, I really wonder what the difference between curvilinear coordinates in a Euclidean space and embedding a curved space into Euclidean space is ???? They resemble to each other for me, so Could you explain or spell out the difference???? Thanks in advance....

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Orodruin
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An embedding is usually of a lower-dimensional manifold. Curvilinear coordinates are used to describe the Euclidean space itself.

wrobel
You can not introduce Euclidian local coordinates in a curved space

I think curvilinear coordinates generally define tangent space, but in curved space also defines normal component besides the tangent space. Am I right??? I saw some close definition like this. Is it true???

wrobel
why do not you study the definition of the manifold first?

wrobel
By definition the Euclidean coordinates are the local coordinates ##x^i## on a manifold such that ##\nabla_i\equiv \frac{\partial }{\partial x^i}##

Orodruin
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