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How can we represent covariant and contravariant vectors on curved spacetime diagrams?

How can we draw these vectors on a spacetime diagram?

Contravariant vectors are really vectors,

therefore we can represent them on the diagram with directed line elements.

Covariant vectors are linear functions acting on contravariant vectors,

therefore the basis of a covariant system

can be represented also with directed line elements, I think,

because these functions can be see as scalar products.

The main question: what is the basis unit vectors on the diagram?

I think that contravariant unit vectors are parallel

to the x=const coordinate curves on the diagram,

and covariant basis unit vectors are orthogonal to it.

Am I right?

But this is just its direction, what about its length (on the diagram)?

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# Representation of covariant and contravariant vectors on spacetime diagrams

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