Einstein and Conformally Flat Critical Metrics of the Volume Functional

Warped product and quasi-Einstein metrics

Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...

Volume and Area Renormalizations for Conformally Compact Einstein Metrics

Quantum effective action from the AdS/CFT correspondence

We obtain an Einstein metric of constant negative curvature given an arbitrary boundary metric in three dimensions, and a conformally flat one given an arbitrary conformally flat boundary metric in other dimensions. In order to compute the on-shell value of the gravitational action for these solutions, we propose to integrate the radial coordinate from the boundary till a critical value where t...

5 v 1 5 D ec 1 99 6 Einstein - Weyl structures corresponding to diagonal Kähler Bianchi IX metrics

We analyse in a systematic way the four dimensionnal Einstein-Weyl spaces equipped with a diagonal Kähler Bianchi IX metric. In particular, we show that the subclass of EinsteinWeyl structures with a constant conformal curvature is the one with a conformally flat but not necessarily flat metric ; we exhibit its 3-parameter distance and Weyl one-form. This extends previous analysis of Pedersen e...

Einstein -Weyl structures corresponding to diagonal Kähler Bianchi IX metrics

We analyse in a systematic way the four dimensionnal Einstein-Weyl spaces equipped with a diagonal Kähler Bianchi IX metric. In particular, we show that the subclass of EinsteinWeyl structures with a constant conformal scalar curvature is the one with a conformally scalar flat but not necessarily scalar flat metric ; we exhibit its 3-parameter distance and Weyl one-form. This extends previous a...