TITLE: Ricci curvature of the Grassmannian?
QUESTION [5 upvotes]: Let $G(k, \mathbb{C}^n)$ be the Grassmannian of $k-$dimensional complex linear subspaces of $\mathbb{C}^n.$  We know that the Grassmannian can be embedded to the projective space $(\mathbb{P}^N,\omega_{FS})$ for some $N,$ via the Plucker embedding.
What can we say about the Ricci curvature of the Grassmannian? or even the scalar curvature? (any bounds?)

REPLY [3 votes]: There even exist explicit calculations of the sectional curvatures of the Grassmannian. Standard references dates back at least to the following in the 60s:
Wong, Yung-Chow. "Differential geometry of Grassmann manifolds." Proceedings of the National Academy of Sciences 57, no. 3 (1967): 589-594.
Wong, Yung-Chow. "Sectional curvatures of Grassmann manifolds." Proceedings of the National Academy of Sciences 60, no. 1 (1968): 75-79.