A proof of uniqueness of the Taub-bolt instanton

We show that the Riemannian Schwarzschild and the "Taub-bolt" instanton sol utions are the only spaces (M, g(mu nu)) such that: M is a four-dimensional, simply connected manifold with a Riemannian, Ricci -flat C-2-metric g(mu nu) which admits (at least) a 1-parameter group mu(ta u) of isometries without isolated fixed points on M. The quotient (M \ L-M)/mu(tau) (where L-M is the set of fixed points of mu( tau)) is an asymptotically flat manifold, and the length of the Killing fie ld corresponding to mu(tau) tends to a constant at infinity. (C) 1999 Publi shed by Elsevier Science B.V. All right reserved, Subj. Class.: Differentia l geometry 1991 MSG: 53C25.