Three-dimensional positively curved generalized Ricci solitons with SO(3)-symmetries

Abstract

We prove the existence of a one-parameter family of pairwise non-isometric, complete, positively curved, steady generalized Ricci solitons of gradient type on ${\mathbb{R}}^3$ that are invariant under the natural cohomogeneity one action of SO(3). In the context of generalized Ricci flow, this result represents the analogue of Bryant's construction of the complete rotationally invariant steady soliton for the Ricci flow.

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• A Gradient Flow for Worldsheet Nonlinear Sigma Models
• Generalized Kahler Geometry and the Pluriclosed Flow
• The Gibbons-Hawking ansatz in generalized Kähler geometry
• Infinite families of homogeneous Bismut Ricci flat manifolds
• The Stability of Generalized Ricci Solitons