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]

In this paper, we classify 8-dimensional manifolds M admitting an SU(3) action of cohomogeneity one such that (i) M is simply connected and the orbit space M/G is isomorphic to [0, 1], and (ii) M/G ∼= S and the principal orbits are simply connected. We discuss applications to the study of the group manifold SU(3) and to 8-dimensional quaternion-Kähler spaces. MSC classification: 57S25; 22E46, 5...

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.

Asymptotically locally conical (ALC) metric of exceptional holonomy has an asymptotic circle bundle structure that accommodates the M theory circle in type IIA reduction. Taking Spin(7) metrics of cohomogeneity one as explicit examples, we investigate deformations of ALC metrics, in particular that change the asymptotic S radius related to the type IIA string coupling constant. When the canonic...

We consider cohomogeneity one homogeneous disk bundles and adress the question when these admit a nonnegatively curved1 invariant metric with normal collar, i.e., such that near the boundary the metric is the product of an interval and a normal homogeneous space. If such a bundle is not (the quotient of) a trivial bundle, then we show that its rank has to be in {2, 3, 4, 6, 8}. Moreover, we giv...

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