This is a corrected version of my paper published in Journal of Geometry and Physics 25(1998), 205-226. I added missing cases to the classification theorem 1.1, namely the SO(n + 1)-manifold SO(n + 2)/(SO(n) × SO(2)), the SO(3)-manifold CP 2 and the SU(3)-manifold CP 1 × CP . Preface Christopher T. Woodward, in his review MR1619843 in MathSciNet, pointed out a gap in the classification of compa...

We analyse in a systematic way the (non-)compact n-dimensional Einstein-Weyl spaces equipped with a cohomogeneity-one metric. In that context, with no compactness hypothesis for the manifold on which lives the Einstein-Weyl structure, we prove that, as soon as the (n-1)-dimensional space is a homogeneous reductive Riemannian space with a unimodular group of left-acting isometries G : • there ex...

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we realize all possible de...

We present a simple derivation of the Ricci-flat Kähler metric and its Kähler potential on the canonical line bundle over arbitrary Kähler coset space equipped with the Kähler-Einstein metric. ∗ E-mail: [email protected] † E-mail: [email protected] ‡ E-mail: [email protected]

Abstract In five dimensions we consider a general shift symmetric and parity preserving scalar tensor action that contains up to second order covariant derivatives of the field. A rotating stealth black hole solution is constructed where metric given by Myers–Perry spacetime with equal momenta field identified Hamilton–Jacobi potential. This nontrivial has an extra hair associated rest mass tes...

We analyse in a systematic way the (non-)compact n-dimensional Einstein-Weyl spaces equipped with a cohomogeneity-one metric. In that context, with no compactness hypothesis for the manifold on which lives the Einstein-Weyl structure, we prove that, as soon as the (n-1)-dimensional basis space is an homogeneous reductive Riemannian space with an unimodular group of left-acting isometries G : • ...