The \(L^ 2\)-metric on the moduli space of \(\text{SU}(2)\)-instantons with instanton number 1 over the Euclidean 4-space. (English) Zbl 0815.53038
Let \({\mathcal M}_ 1(Q)\) denote the moduli space of self-dual SU(2)- connections with instanton number 1 over \(\mathbb{R}^ 4\). The main result of the paper shows that \({\mathcal M}_ 1(Q)\) regarded as a Riemannian manifold is isometric to \(\mathbb{R}^ + \times \mathbb{R}^ 4\).
Reviewer: D.Motreanu (Iaşi)
MSC:
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 58D27 | Moduli problems for differential geometric structures |
References:
| [1] | Atiyah, M.F.:Geometry of Yang-Mills fields. Scuola Normale Superiore, Pisa 1979. · Zbl 0435.58001 |
| [2] | Babadshanjan, F.;Habermann, L.: A family of metrics on the moduli space of BPST-instantons.Ann. Global Anal. Geom. 9 (1991), 245-252. · Zbl 0748.53014 · doi:10.1007/BF00136814 |
| [3] | Bérard-Bergery, L.: Sur de nouvelles variétés riemannienes d’Einstein.Publications de l’Institut Elie Cartan, Nancy,4 (1982), 1-60. |
| [4] | Bishop, R.L.;O’Neill, B.: Manifolds of negative curvature.Trans. Am. Math. Soc. 145 (1969), 1-49. · Zbl 0191.52002 · doi:10.1090/S0002-9947-1969-0251664-4 |
| [5] | Doi, H.;Matsumoto, Y.;Matsumoto, T.:An explicit formula of the metric on the moduli space of BPST-instantons over S 4.A Fête of Topology. Academic Press, New York 1987. · Zbl 0658.58005 |
| [6] | Eichhorn, J.: Yang-Mills-Theorie über offenen Riemannschen Mannigfaltigkeiten.Rend. Circ. Mat. Palermo (2)9 (1985), 61-72. · Zbl 0661.53031 |
| [7] | Eichhorn, J.: Invariance properties of the Laplace operator.Rend. Circ. Mat. Palermo (2)22 (1990), 35-47. · Zbl 0717.53028 |
| [8] | Groisser, D.: The geometry of the moduli space of CP2 instantons.Invent. Math. 99 (1990), 393-409. · doi:10.1007/BF01234425 |
| [9] | Groisser, D.:Parker, T.H.: The Riemannian geometry of the Yang-Mills moduli space.Commun. Math. Phys. 112 (1987), 663-689. · Zbl 0637.53037 · doi:10.1007/BF01225380 |
| [10] | Groisser, D.;Parker, T.H.: The geometry of the Yang-Mills moduli space for definite manifolds.J. Differential Geom. 29 (1989), 499-544. · Zbl 0679.53024 |
| [11] | Habermann, L.: On the geometry of the space ofSp(1)-instantons with Pontrajagin index 1 on the 4-sphere.Ann. Global Anal. Geom. 6 (1988), 3-29. · Zbl 0667.53053 · doi:10.1007/BF00054606 |
| [12] | Habermann, L.: A family of metrics on the moduli space of CP2 instantons.Commun. Math. Phys. (to appear). · Zbl 0777.53038 |
| [13] | Taubes, C. H.: Stability in Yang-Mills theories.Commun. Math. Phys. 91 (1983), 235-263. · Zbl 0524.58020 · doi:10.1007/BF01211160 |
| [14] | Uhlenbeck, K.: Removable singularities in Yang-Mills fields.Commun. Math. Phys. 83 (1982), 11-29. · Zbl 0491.58032 · doi:10.1007/BF01947068 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
