Inspired by the example of Abdelqader and Lake for the Kerr metric, we construct local scalar polynomial curvature invariants that vanish on the horizon of any stationary black hole: the squared norms of the wedge products of n linearly independent gradients of scalar polynomial curvature invariants, where n is the local cohomogeneity of the spacetime.

By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many nontrivial complete Hamiltonian minimal submanifolds in CP n and Cn.

We construct infinitely many new 1-parameter families of simply connected complete non-compact G$\_2$-manifolds with controlled geometry at infinity. The generic member each family has so-called asymptotically locally conical (ALC) geometry. However, the nature asymptotic changes two special parameter values: one value we obtain a unique (AC) geometry; on approach to other metrics collapses an ...

In this paper we construct new examples of minimal Lagrangian submanifolds in the complex hyperbolic space with large symmetry groups, obtaining three 1-parameter families with cohomogeneity one. We characterize them as the only minimal Lagrangian submanifolds in CHn foliated by umbilical hypersurfaces of Lagrangian subspaces RHn of CHn. Several suitable generalizations of the above constructio...

We prove an existence result for the prescribed Ricci curvature equation certain doubly warped product metrics on $$\mathbb {S}^{d_1+1}\times \mathbb {S}^{d_2}$$ , where $$d_i \ge 2$$ . If T is a metric satisfying assumptions, we show that can be scaled independently two factors so as to itself tensor of some metric. This first global problem closed cohomogeneity one manifolds since work Hami...

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...

We construct the normal forms of null-K\"ahler metrics: pseudo-Riemannian metrics admitting a compatible parallel nilpotent endomorphism tangent bundle. Such are examples non-Riemannian holonomy reduction, and (in complexified setting) appear in Bridgeland stability conditions moduli spaces Calabi-Yau three-folds. Using twistor methods we show that, dimension four - where there is connection wi...