Cohomogeneity-one G2-structures

Journal of Geometry and Physics

Volumn 44, Issue 2-3, 2002, Pages 202-220

  Cleyton, Richard ^a   Swann, Andrew ^a  

^a UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

Author keywords

Cohomogeneity one; G2; Holonomy; Weak holonomy

Indexed keywords

EID: 0036888101     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(02)00074-8     Document Type: Article

References (22)

1. L. Bérard Bergery, Sur de nouvelles variétés riemanniennes d'Einstein, Vol. 6, Publications de l'Institut É. Cartan, Nancy, 1982, pp. 1-60.
2. A.L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3, Folge, Vol. 10, Springer, Berlin, 1987.
3. 2 holonomy metrics, June 2001. eprint arXiv:hep-th/0106034.
4. G.E. Bredon, Introduction to compact transformation groups, Pure Appl. Math. 46 (1972).
5. R.L. Bryant, Metrics with exceptional holonomy, Ann. Math. 126 (1987) 525-576.
6. R.L. Bryant, Classical, exceptional, and exotic holonomies: a status report, Actes de la Table Ronde de Géométrie Différentielle, Luminy, 1992, Paris, Sémin. Congr., Vol. 1, Soc. Math. France, 1996, pp. 93-165.
7. R.L. Bryant, S.M. Salamon, On the construction of some complete metrics with exceptional holonomy, Duke Math. J. 58 (1989) 829-850.
8. 2-structures, J. London Math. Soc. 53 (1996) 407-416.
9. R. Cleyton, G-structures and Einstein metrics, Ph.D. Thesis, University of Southern Denmark, Odense, 2001. ftp://ftp.imada.sdu.dk/pub/phd/2001/24.PS.gz.
10. M. Cvetič, G.W. Gibbons, H. Lü, C.N. Pope, New cohomogeneity-one metrics with Spin(7) holonomy, May 2001. eprint arXiv:math.DG/0105119.
11. 2-structures, J. Geom. Phys. 23 (3-4) (1997) 259-286.
12. G. Glaeser, Fonctions composées différentiables, Ann. Math. 77 (2) (1963) 193-209.
13. A. Gray, Weak holonomy groups, Math. Z. 123 (1971) 290-300.
14. N.J. Hitchin, Stable forms and special metrics, in: M.A. Fernández, J.A. Wolf (Eds.), Global Differential Geometry: The Mathematical Legacy of Alfred Gray, Am. Math. Soc., Providence, RI, 2001.
15. 2. I, J. Diff. Geom. 43 (1996) 291-328.
16. 2. II, J. Diff. Geom. 43 (1996) 329-375.
17. D. Joyce, Compact Manifolds with Special Holonomy, Oxford Mathematical Monographs, Oxford University Press, 2000.
18. J.L. Kazdan, F.W. Warner, Curvature functions for open 2-manifolds, Ann. Math. 99 (2) (1974) 203-219.
19. A. Kovalev, Twisted connected sums and special Riemannian holonomy, Preprint MS-00-011, University of Edinburgh, December 2000. eprint arXiv:math.DG/0012189.
20. P.S. Mostert, On a compact Lie group acting on a manifold, Ann. Math. 65 (1957) 447-455;
21. P.S. Mostert, On a compact Lie group acting on a manifold, Ann. Math. 66 (1957) 589.
22. A.F. Swann, Hyper-Kähler and quaternionic Kähler geometry, Math. Ann. 289 (1991) 421-450.