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# Riemann Curvature Tensor watch

1. i'm trying to show that
the proof says:
Note for an arbitrary dual vector field and any derivative operator we have
this equation can be proven from

where the ordinary derivative has been substituted for and we have made use of the commutativity of ordinary derivatives and the symmetry of . In differential forms notation this statement is . Thus,

now i have quite a lot of problems following this:
(i) terminology: it talks about as a dual vector field. now apparently there are two types of dual space - algebraic dual space and continuous dual space. if its the algebraic one then we can refer to it as a 1 form. my question here is basically which is it? am i entitled to call it a 1 form?

(ii)ok so i have no idea how to get to
using the method they descirbe.

(iii) i assume that since , they just double both sides to get but then why is
?

thanks

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Updated: October 13, 2009
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