Special cohomogeneity-one metrics with Q1,1,1 or M1,1,0 as the principal orbit

Equivariant Principal Bundles over Spheres and Cohomogeneity One Manifolds

We classify SO(n)-equivariant principal bundles over Sn in terms of their isotropy representations over the north and south poles. This is an example of a general result classifying equivariant (Π, G)-bundles over cohomogeneity one manifolds.

Calabi-Yau Manifolds of Cohomogeneity One as Complex Line Bundles

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]

On the Geometry of Cohomogeneity One Manifolds with Positive Curvature

There are very few known examples of manifolds with positive sectional curvature. Apart from the compact rank one symmetric spaces, they exist only in dimensions 24 and below and are all obtained as quotients of a compact Lie group equipped with a biinvariant metric under an isometric group action. They consist of certain homogeneous spaces in dimensions 6, 7, 12, 13 and 24 due to Berger [Be], ...

Existence of extremal metrics on almost homogeneous manifolds of cohomogeneity one – IV

This paper is the first of a series of papers in which we generalize our results in (Asian J. of Math. 4, 817–830 (2000); J. Geom. Anal. 12, 63–79 (2002); Intern. J. Math. 14, 259–287 (2003)) to the general complex compact almost homogeneous manifolds of real cohomogeneity one. In this paper we deal with the exceptional case of the G2 action (Cf. Intern. J. Math. 14, 259–287 (2003), p. 285). In...

Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One∗