Explicit self-dual metrics on $\mathbb{CP}_2 \# \cdots\#\mathbb{CP}_2$

Explicit Self - Dual Metrics On

We display explicit half-conformally-flat metrics on the connected sum of any number of copies of the complex projective plane. These metrics are obtained from magnetic monopoles in hyperbolic 3-space by an analogue of the Gibbons-Hawking ansatz, and are conformal compactifications of asymptotically-flat, scalar-flat Kahler metrics on «-fold blow-ups of C . The corresponding twistor spaces are ...

Toric Self-dual Einstein Metrics as Quotients

We use the quaternion Kähler reduction technique to study old and new selfdual Einstein metrics of negative scalar curvature with at least a two-dimensional isometry group, and relate the quotient construction to the hyperbolic eigenfunction Ansatz. We focus in particular on the (semi-)quaternion Kähler quotients of (semi-)quaternion Kähler hyperboloids, analysing the completeness and topology,...

Self-dual Metrics and Twenty-eight Bitangents

We prove that there is a one-to-one correspondence between selfdual metrics on 3CP of positive scalar curvature admitting a non-trivial Killing field but not being conformal to LeBrun metrics, and a class of normal quartic surfaces in CP whose equations can be explicitly written down. As a consequence, we show that the moduli space of these self-dual metrics on 3CP is non-empty and diffeomorphi...

New Examples of Einstein Self-dual Metrics

Almost - Kähler Anti - Self - Dual Metrics

of the Dissertation Almost-Kähler Anti-Self-Dual Metrics by Inyoung Kim Doctor of Philosophy in Mathematics Stony Brook University 2014 We show the existence of strictly almost-Kähler anti-self-dual metrics on certain 4-manifolds by deforming a scalar-flat Kähler metric. On the other hand, we prove the non-existence of such metrics on certain other 4-manifolds by means of SeibergWitten theory. ...