On the Kähler geometry of the Hilbert-Schmidt Grassmannian
In this paper the author considers a geometry of some infinite- dimensional manifolds. He computes the Riemann curvature tensor of the Hilbert-Schmidt Grassmannian endowed with its natural Kähler structure. It is shown that the sectional curvature is non-negative, but not strictly. The author proves also that the sectional curvature of the Hilbert-Schmidt space of almost complex structures is non-positive, but not strictly.
scientific article; zbMATH DE number 4117491