Einstein metrics and Yamabe invariants of weighted projective spaces

Projective Invariant Metrics for Einstein Spaces

λ-Projectively Related Finsler Metrics and Finslerian Projective Invariants

In this paper, by using the concept of spherically symmetric metric, we defne the notion of λ-projectively related metrics as an extension of projectively related metrics. We construct some non-trivial examples of λ-projectively related metrics. Let F and G be two λ-projectively related metrics on a manifold M. We find the relation between the geodesics of F and G and prove that any geodesic of...

Isospectral Metrics on Weighted Projective Spaces

We construct the first examples of families of bad Riemannian orbifolds which are isospectral with respect to the Laplacian but not isometric. In our case these are particular fixed weighted projective spaces equipped with isospectral metrics obtained by a generalization of Schüth’s version of the torus method.

Einstein Metrics and the Yamabe Problem

Which smooth compact n-manifolds admit Riemannian metrics of constant Ricci curvature? A direct variational approach sheds some interesting light on this problem, but by no means answers it. This article surveys some recent results concerning both Einstein metrics and the associated variational problem, with the particular aim of highlighting the striking manner in which the 4-dimensional case ...

Kähler–einstein Metrics on Log Del Pezzo Surfaces in Weighted Projective 3–spaces

A log del Pezzo surface is a projective surface with quotient singularities such that its anticanonical class is ample. Such surfaces arise naturally in many different contexts, for instance in connection with affine surfaces [Miyanishi81], moduli of surfaces of general type [Alexeev94], 3 and 4 dimensional minimal model program [Alexeev93]. They also provide a natural testing ground for existe...