Vol. 253, No. 2, 2011

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Type II almost-homogeneous manifolds of cohomogeneity one

Daniel Guan

Vol. 253 (2011), No. 2, 383–422
Abstract

This paper continues our investigation on the existence of extremal metrics of the general affine and type II almost-homogeneous manifolds of cohomogeneity one. It deals with the general type II cases with hypersurface ends: more precisely, with manifolds having certain Pn × (Pn)- or P2-bundle structures. In particular, we study the existence of Kähler–Einstein metrics on these manifolds and obtain new Kähler–Einstein manifolds as well as Fano manifolds without Kähler–Einstein metrics.

Keywords
almost-homogeneous manifold, Kähler–Einstein metric, Fano manifold, extremal metric, fourth-order differential equation, cohomogeneity one, fiber bundle, existence, Futaki invariant, geodesic stability
Mathematical Subject Classification 2000
Primary: 14M17, 32L05, 32M12, 53C10, 53C21
Secondary: 32Q20, 53C55, 53C26
Milestones
Received: 2 April 2009
Revised: 27 May 2011
Accepted: 11 July 2011
Published: 21 January 2012
Authors
Daniel Guan
Department of Mathematics
University of California
Riverside, CA 92521
United States
http://www.math.ucr.edu/~zguan