On Ricci solitons of cohomogeneity one

TL;DR

This paper investigates cohomogeneity one Ricci solitons, deriving new explicit examples of complete Kahler Ricci solitons of various types, characterized by specific geometric foliations involving circle bundles and Fano manifolds.

Contribution

It introduces new explicit examples of complete Kahler Ricci solitons using cohomogeneity one ansatze, expanding the known classes of such solitons.

Findings

Constructed explicit examples of complete Kahler Ricci solitons

Classified solitons as expanding, steady, and shrinking types

Described geometric structures involving circle bundles over Fano manifolds

Abstract

We analyse some properties of the cohomogeneity one Ricci soliton equations, and use Ansatze of cohomogeneity one type to produce new explicit examples of complete Kahler Ricci solitons of expanding, steady and shrinking types. These solitons are foliated by hypersurfaces which are circle bundles over a product of Fano Kahler-Einstein manifolds or over coadjoint orbits of a compact connected semisimple Lie group.