On the Ricci Iteration for Homogeneous Metrics on Spheres and Projective Spaces

The prescribed cross curvature problem on the three-sphere

“…Our next theorem reveals that λ(g) increases as one passes from g to X(g). Several results of this nature are known for the Ricci curvature; see, e.g., [28,8]. with equality holding if and only if g = ρg 0 for some ρ > 0.…”

On the symmetries of Siklos spacetimes

“…These notions were first introduced with reference to Kähler metrics [29] and then considered in Riemannian settings, with particular regard to homogeneous spaces ( [3,28]). It is essential that the iteration preserves the signature of the metric, which makes Ricci iterations a quite rare phenomenon.…”

Ricci Flow on Torus Bundles

“…This issue can be overcome by requiring additional structure, such as a large isometry group, since Ricci flow must preserve isometry. An example of requiring a large isometry group is the work done on Ricci flow on homogeneous manifolds [Lau13,BPRZ21].…”