A Reimann Tensor in Component Form?

Summary
Can someone explain the component form of the Riemann tensor as shown in the picture?
So I was reading the Charles&Wheeler book and this came out of nowhere:
but how is it derived in the wholeness?
IMG_4634.jpg
 

Orodruin

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I am sorry, but it is unclear to me exactly what you are having problems with. Please be more specific in your questions.
 
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how is it derived in the wholeness?
As noted in the book, exercise 11.3 helps you to derive the component form. You should work through that exercise, and then ask more specific questions if you get stuck somewhere. As you ask it here, your question is much too broad.

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