1. A new construction of anti-self-dual four-manifolds.
- Author
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Moraru, Dan
- Subjects
- *
RIEMANNIAN manifolds , *PENROSE transform , *TWISTOR theory , *SPINOR analysis , *METRIC system - Abstract
We describe a new construction of anti-self-dual metrics on four-manifolds. These metrics are characterized by the property that their twistor spaces project as affine line bundles over surfaces. To any affine bundle with the appropriate sheaf of local translations, we associate a solution of a second-order partial differential equations system D2 V = 0 on a five-dimensional manifold $${\mathbf{Y}}$$. The solution V and its differential completely determine an anti-self-dual conformal structure on an open set in { V = 0}. We show how our construction applies in the specific case of conformal structures for which the twistor space $${\mathcal{Z}}$$ has $${ \dim\left|-\frac{1}{2}K_\mathcal{Z}\right|\geq 2}$$, projecting thus over $${\mathbb C\mathbb P_2}$$ with twistor lines mapping onto plane conics. [ABSTRACT FROM AUTHOR]
- Published
- 2010
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