Uniqueness of constant scalar curvature Sasakian metrics

Constant scalar curvature metrics with isolated singularities

We extend the results and methods of [6] to prove the existence of constant positive scalar curvature metrics g which are complete and conformal to the standard metric on S \ Λ, where Λ is a disjoint union of submanifolds of dimensions between 0 and (N − 2)/2. The existence of solutions with isolated singularities occupies the majority of the paper; their existence was previously established by...

Constant scalar curvature metrics on toric surfaces

On the existence of Kähler metrics of constant scalar curvature

For certain compact complex Fano manifolds M with reductive Lie algebras of holomorphic vector fields, we determine the analytic subvariety of the second cohomology group of M consisting of Kähler classes whose Bando-Calabi-Futaki character vanishes. Then a Kähler class contains a Kähler metric of constant scalar curvature if and only if the Kähler class is contained in the analytic subvariety....

Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes

In this paper we give examples of constant scalar curvature metrics on piecewise-flat triangulated 3-manifolds. These types of metrics are possible candidates for “best” metrics on triangulated 3-manifolds. In the pentachoron, the triangulation formed by the simplicial boundary of the 4-simplex, we find that its stucture is completely deterimed with a vertex transitive metric. Further this metr...

Kähler Metrics of Constant Scalar Curvature on Hirzebruch Surfaces

It is shown that a Hirzebruch surface admits a Kähler metric (possibly indefinite) of constant scalar curvature if and only if its degree equals zero. There have been many extensive studies for positive-definite Kähler metrics of constant scalar curvature, especially, Kähler Einstein metrics and scalar-flat Kähler metrics, on existence, uniqueness, obstructions, and relationships with other not...