Einstein metrics, projective structures and the SU(∞) Toda equation

JOURNAL OF GEOMETRY AND PHYSICS

卷:147

Article

Dunajski, Maciej¹  Waterhouse, Alice¹ 

[1] Univ Cambridge, Dept Appl Math & Theoret Phys, Wilberforce Rd, Cambridge CB3 0WA, England

关键词: Projective structures;    Self-duality;    Integrability;   

DOI  :  10.1016/j.geomphys.2019.103523

来源: Elsevier

【 摘 要 】

We establish an explicit correspondence between two-dimensional projective structures admitting a projective vector field, and a class of solutions to the SU(infinity) Toda equation. We give several examples of new, explicit solutions of the Toda equation, and construct their mini-twistor spaces. Finally we discuss the projective-to-Einstein correspondence, which gives a neutral signature Einstein metric on a cotangent bundle T*N of any projective structure (N, [del]). We show that there is a canonical Einstein of metric on an Fe-bundle over T*N, with a connection whose curvature is the pull-back of the natural symplectic structure from T*N. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free