The four-dimensional Kerr-de Sitter and Kerr-AdS black hole metrics have cohomogeneity 2, and they admit a generalisation in which an additional parameter characterising a NUT charge is included. In this paper, we study the higher-dimensional Kerr-AdS metrics, specialised to cohomogeneity 2 by appropriate restrictions on their rotation parameters, and we show how they too admit a generalisation...

For a compact connected Lie group G acting as isometries of cohomogeneity not equal to 0 or 2 on orientable Riemannian manifold $$M^{n+1},$$ we prove the existence nontrivial embedded G-invariant minimal hypersurface, that is smooth outside set Hausdorff dimension at most $$n-7.$$

We show that noncompact homogeneous spaces not diffeomorphic to Euclidean space of dimension 9 or 10 admit no Einstein metrics negative Ricci curvature, with only three potential exceptions. The main ingredient in the proof is show, via a cohomogeneity-one approach, admitting an ideal isomorphic $ \mathfrak{sl}_2(\mathbb{R}) curvature.

We consider the nonlinear stability of the Kaluza-Klein monopole viewed as the static solution of the five-dimensional vacuum Einstein equations. Using both numerical and analytical methods, we give evidence that the Kaluza-Klein monopole is asymptotically stable within the cohomogeneity-two biaxial Bianchi type-IX ansatz recently introduced by Bizoń, Chmaj, and Schmidt. We also show that for s...