Fine, J;
Krasnov, K;
Singer, M;
(2021)
Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition.
Mathematische Annalen
, 379
pp. 569-588.
10.1007/s00208-020-02097-z.
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Abstract
Let (M,g) be a compact oriented Einstein 4-manifold. Write R_{+} for the part of the curvature operator of g which acts on self-dual 2-forms. We prove that if R_{+} is negative definite then g is locally rigid: any other Einstein metric near to g is isometric to it. This is a chiral generalisation of Koiso's Theorem, which proves local rigidity of Einstein metrics with negative sectional curvatures. Our hypotheses are roughly one half of Koiso's. Our proof uses a new variational description of Einstein 4-manifolds, as critical points of the so-called poure connection action S. The key step in the proof is that when R_{+} < 0, the Hessian of S is strictly positive modulo gauge.
| Type: | Article |
|---|---|
| Title: | Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00208-020-02097-z |
| Publisher version: | https://doi.org/10.1007/s00208-020-02097-z |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10112563 |
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