Asymptotically cylindrical 7-manifolds of holonomy G2 with applications to compact irreducible G2-manifolds

被引：0

作者：

Alexei Kovalev

Johannes Nordström

机构：

[1] University of Cambridge,DPMMS

[2] Centre for Mathematical Sciences,Department of Mathematics, South Kensington Campus

[3] Imperial College,undefined

来源：

Annals of Global Analysis and Geometry | 2010年 / 38卷

关键词：

Special holonomy; -manifolds; Asymptotically cylindrical manifolds; Moduli spaces; Coassociative submanifolds;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We construct examples of exponentially asymptotically cylindrical (EAC) Riemannian 7-manifolds with holonomy group equal to G2. To our knowledge, these are the first such examples. We also obtain EAC coassociative calibrated submanifolds. Finally, we apply our results to show that one of the compact G2-manifolds constructed by Joyce by desingularisation of a flat orbifold T7/Γ can be deformed to give one of the compact G2-manifolds obtainable as a generalized connected sum of two EAC SU(3)-manifolds via the method of Kovalev (J Reine Angew Math 565:125–160, 2003).

引用

页码：221 / 257

页数：36

共 29 条

[1]

Berger M.(1955)Sur les groupes d’holonomie homogène des variétés à connexion affines et des variétés riemanniennes Bull. Soc. Math. France 83 279-330

[2]

Bryant R.L.(1987)Metrics with exceptional holonomy Ann. Math. 126 525-576

[3]

Bryant R.L.(1989)On the construction of some complete metrics with exceptional holonomy Duke Math. J. 58 829-850

[4]

Salamon S.M.(2006)Desingularizations of Calabi–Yau 3-folds with a conical singularity Q. J. Math. 57 151-181

[5]

Chan Y.-M.(1971)The splitting theorem for manifolds of non-negative Ricci curvature J. Diff. Geom. 6 119-128

[6]

Cheeger J.(1978)Asymptotically flat self-dual solutions to Euclidean gravity Phys. Lett. B 74 249-251

[7]

Gromoll D.(1990)Einstein metrics on Comm. Math. Phys. 127 529-553

[8]

Eguchi T.(1982), Acta Math. 148 47-157

[9]

Hanson A.J.(1987) and Proc. Lond. Math. Soc. 55 59-126

[10]

Gibbons G.W.(1997) bundles Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 503-515

← 1 2 3 →