biVector forum

Help with calculations with Differential Geometric Algebra and sources

Hi, I’m new to the forum and I am eager to see what information there is around, but first I would like to ask the question that brought me here.

I am trying to learn General Relativity with Geometric Algebra. Following the article Spacetime Geometry with Geometric Calculus but I am finding some algebraic problems when dealing with expressions like the following, eq(96)

$$\partial_a \cdot (\dot{D} \wedge \dot{R}(a \wedge b))= \dot{R}(\dot{D} \wedge b) - D \wedge R(b) = 0$$

Being D the covariant derivative operator and R(a \wedge b) the Riemann tensor.

How does the D operator enter in the argument of the Riemann tensor? and why the minus sign in the Ricci tensor element?

Can you recommend a good book where these operations are well introduced and explained? I have read through Clifford Algebra to Geometric Calculus and Geometric Algebra for physicists but I haven’t found proper explanations about how these operations are performed

Thank you in advance!

I don’t know why it didn’t get into LaTex

\partial_a \cdot (\dot{D} \wedge \dot{R}(a \wedge b))= \dot{R}(\dot{D} \wedge b) - D \wedge R(b) = 0