On the mass of static metrics with positive cosmological constant - I

In this paper we propose and discuss a notion of mass for compact static metrics with positive cosmological constant. As a consequence, we characterise the de Sitter solution as the only static vacuum metric with zero mass. Finally, we show how to adapt our analysis to the case of negative cosmological constant, leading to a uniqueness theorem for the Anti de Sitter spacetime.Comment: 34 pages, 3 figure

On the resolution of extremal and constant scalar curvature Kaehler orbifolds

In this paper we give sufficient conditions on a compact orbifold with an extremal Kaehler metric to admit a resolution with an extremal Kaehler metric. We also complete the Kaehler constant scalar curvature case.Comment: This paper, together with the next one by the same authors, contains more general results than arxiv.org/abs/1402.5919 (by the same authors), which will then be withdraw

A note on Codazzi tensors

We discuss a gap in Besse's book, recently pointed out by Merton, which concerns the classification of Riemannian manifolds admitting a Codazzi tensors with exactly two distinct eigenvalues. For such manifolds, we prove a structure theorem, without adding extra hypotheses and then we conclude with some application of this theory to the classification of three-dimensional gradient Ricci solitons.Comment: Minor correction