We classify, up to orbit equivalence, the cohomogeneity one actions on the noncompact Riemannian symmetric spaces G2 /G2, SL3(C)/SU3 and SO 2,n+2/SO2SOn+2, n ≥ 1.

The remarkable and unexpected separability of the Hamilton-Jacobi and Klein-Gordon equations in the background of a rotating four-dimensional black hole played an important rôle in the construction of generalisations of the Kerr metric, and in the uncovering of hidden symmetries associated with the existence of Killing tensors. In this paper, we show that the Hamilton-Jacobi and Klein-Gordon eq...

We characterize cohomogeneity one manifolds and homogeneous spaces with a compact Lie group action admitting an invariant metric positive scalar curvature.

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 consider compact manifolds $M$ with a cohomogeneity one action of Lie group $G$ such that the orbit space $M/G$ is closed interval. For $T$ maximal torus $G$, we find necessary and sufficient conditions on diagram $T$-action GKM type, describe its graph. The general results are illustrated explicit examples.