Ricci-Flat Anti-Self-Dual Asymptotically Locally Euclidean 4-Manifolds
نویسندگان
چکیده
of the Dissertation Ricci-Flat Anti-Self-Dual Asymptotically Locally Euclidean 4-Manifolds by Evan Patrick Wright Doctor of Philosophy in Mathematics Stony Brook University 2013 A classification result for Ricci-flat anti-self-dual asymptotically locally Euclidean 4-manifolds is obtained: they are either hyperkähler (one of the gravitational instantons classified by Kronheimer), or a cyclic quotient of a Gibbons-Hawking space. In the latter case, the action of the deck group is described in terms of the corresponding monopole set in R, and it is shown that every such quotient is Kähler.
منابع مشابه
Conformally flat Einstein-like 4-manifolds and conformally flat Riemannian 4-manifolds all of whose Jacobi operators have parallel eigenspaces along every geodesic
A local classification of all locally conformal flat Riemannian 4-manifolds whose Ricci tensor satisfies the equation ∇ ( ρ− 1 6 sg ) = 1 18 ds⊙ g as well as a local classification of all locally conformal flat Riemannian 4-manifolds for which all Jacobi operators have parallel eigenspaces along every geodesic is given. Non-trivial explicit examples are presented. The problem of local descripti...
متن کاملRicci Flatness of Asymptotically Locally Euclidean Metrics
In this article we study the metric property and the function theory of asymptotically locally Euclidean (ALE) Kähler manifolds. In particular, we prove the Ricci flatness under the assumption that the Ricci curvature of such manifolds is either nonnegative or nonpositive. The result provides a generalization of previous gap type theorems established by Greene and Wu, Mok, Siu and Yau, etc. It ...
متن کاملCompact Anti-self-dual Orbifolds with Torus Actions
We give a classification of toric anti-self-dual conformal structures on compact 4-orbifolds with positive Euler characteristic. Our proof is twistor theoretic: the interaction between the complex torus orbits in the twistor space and the twistor lines induces meromorphic data, which we use to recover the conformal structure. A compact anti-self-dual orbifold can also be constructed by adding a...
متن کاملSelf-Dual Solutions to Euclidean Gravity
The discovery of self-dual instanton solutions in Euclidean Yang-Mills theory [I] has recently stimulated a great deal of interest in self-dual solutions to Einstein’s theory of gravitation. One would expect that the relevant instanton-like metrics would be those whose gravitational fields are self-dual, localized in Euclidean spacetime and free of singularities. In fact, solutions have been fo...
متن کاملNew Brane Solutions from Killing Spinor Equations
In a recent paper, we have pointed out a relation between the Killing spinor and Einstein equations. Using this relation, new brane solutions of D = 11 and D = 10 type IIB supergravity theories are constructed. It is shown that in a brane solution, the flat world-volume directions, the smeared transverse directions and the sphere located at a fixed radial distance can be replaced with any Loren...
متن کامل