there is a short remark in the textbook about GR I have been reading, which has been bugging me for the last few hours:
My questions are:
(1): In multivariable calculus, curl can be intuitively described as the rotation vector of a vector field. Why is it here a (0,2)-tensor field?
(2): How can one derive the second equation from the first equation?
Best regards.
EDIT:
The second equation only holds for vector fields $Y,Z \perp X$.