# Riemann and Ricci

Gold Member
For you math people who like to express objects in a coordinate-free way, how would you denote the Riemann and the Ricci curvature tensors? They are both usually denoted R but with different indices to show which one is which. Is there a standard way to write them without the coordinate indices?

I strongly recommend Doran and Lasenby's "Geometric Algebra for Physicists". They distinguish the two by showing their arguments. The Riemann tensor is a bivector-valued function of a bivector argument, so it can designated R(v1^v2), where ^ is the wedge-product. The Ricci tensor is a vector valued function of a vector argument, so it can be designated R(v).