Regards to all you!

I´m not sure if the formula

about the quantity of independents components of Riemann tensor is right. I think this value must be

I say this because:

(1)

Moreover

and

and

then, there are

components whose value is 0.

The second antisymmetry tells us that

So, there are

components whose vale is 0, but the components

were already counted in (1); and

and

. Then there are

more null components.

So, R has

not-null components (that is, independent components)

But the first antisymmetry

tells us that half the components of R are dependent of another half, so the independent componets are

And the second antisymmetry

tells us the same, so remain

elements. The interchange symmetry

tells the same, so remain

elements.

The Bianchi symmetry

implies that each component depends of another two elements, so only 2/3 of remaining indepependent components are really independent.

Then, finally, there are

independent components in Riemann tensor R.

This is my reasoning. Is there misprint in the book? Am I right or I'm wrong? Please I wish someone answer me.

See you soon!!