We investigate U(1)-equivariant deformations of C. LeBrun's selfdual metric with torus action. We explicitly determine all U(1)-subgroups of the torus for which one can obtain U(1)-equivariant deformations that do not preserve the whole of the torus action. This gives many new self-dual metrics with U(1)-action which are not conformally isometric to LeBrun metrics. We also count the dimension of the moduli space of self-dual metrics with U(1)- action obtained in this way.
ASJC Scopus subject areas
- 数学 (全般)