Thanks for the responses, especially robphy. I'll do a little research about the eigenvalues of R^{i}_j.
Here's how I came across this quantity:
I'm working in a rather specific area: I'm studying the relationship between the curvature of a Kahler supermanifold with the curvature of the...
In my calculations, I come across the scalar
R^{ji} R_{ij} - R^2
(R_{ij} is the Ricci tensor, R is the Ricci scalar)
More specifically, I come across the integral of this scalar over a compact manifold.
Has anyone seen it before, and does it have any nice properties?
John Schulman