G2-structures with torsion from half-integrable nilmanifolds

Journal of Geometry and Physics

Volumn 54, Issue 3, 2005, Pages 262-285

  Chiossi, Simon G ^a   Swann, Andrew ^a  

^a UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

Author keywords

G2 structure; Half integrable SU(3) structure; Nilmanifold; Torsion connection

Indexed keywords

EID: 18444403742     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geomphys.2004.09.009     Document Type: Article

References (45)

1. E. Abbena S. Garbiero S. Salamon Almost Hermitian geometry on six dimensional nilmanifolds Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 30 1 2001 147-170
2. B. Alexandrov, T. Friedrich, and N. Schoemann, Almost Hermitian 6-manifolds revisited, J. Geom. Phys., in press. eprint math.DG/0403131.
3. B. Alexandrov S. Ivanov Vanishing theorems on Hermitian manifolds Diff. Geom. Appl. 14 3 2001 251-265
4. 2 Commun. Math. Phys. 246 1 2004 43-61
5. C. Benson C.S. Gordon Kähler and symplectic structures on nilmanifolds Topology 27 1988 513-518
6. G. Bor L. Hernández Lamoneda Bochner formulae for orthogonal G-structures on compact manifolds Diff. Geom. Appl. 15 3 2001 265-286
7. R.L. Bryant Metrics with exceptional holonomy Ann. Math. 126 1987 525-576
8. 2-structures, May 2003. eprint math.DG/0305124.
9. F. Campana Remarques sur les groupes de Kähler nilpotents Ann. Sci. École Norm. Sup. (4) 28 3 1995 307-316
10. S.G. Chiossi, Special Riemannian structures in dimensions 6 and 7, Ph.D. Thesis, Universities of Genova, Torino and Torino Politecnico, 2003.
11. 2 structures Differential Geometry Valencia, 2001 2002 World Scientific Publishing River Edge, NJ pp. 115-133
12. 2 -structures, June 2003. eprint math.DG/0306362.
13. 2 manifolds with cohomogeneity-one actions of simple Lie groups, in preparation.
14. S. Console A. Fino Dolbeault cohomology of compact nilmanifolds Transform. Groups 6 2 2001 111-124
15. L.A. Cordero M. Fernández A. Gray Symplectic manifolds with no Kähler structure Topology 25 3 1986 375-380
16. L.A. Cordero M. Fernández L. Ugarte Pseudo-Kähler metrics on six-dimensional nilpotent lie algebras J. Geom. Phys. 50 1-4 2004 115-137
17. P. Deligne P. Griffiths J. Morgan D. Sullivan Real homotopy theory of Kähler manifolds Invent. Math. 29 1975 245-274
18. J. Dixmier Cohomologie des algèbres de Lie nilpotentes Acta Sci. Math. Szeged 16 1955 246-250
19. 2 Ann. Mat. Pura Appl. (4) 132 1982 19-45
20. 2 structures, in preparation.
21. A. Fino M. Parton S.M. Salamon Families of strong KT structures in six dimensions Comment. Math. Helv. 79 2 2004 317-340
22. T. Friedrich S. Ivanov Parallel spinors and connections with skew-symmetric torsion in string theory Asian J. Math. 6 2 2002 303-335
23. 2-manifolds J. Geom. Phys. 48 1 2003 1-11
24. 2-structures J. Geom. Phys. 23 3-4 1997 259-286
25. P. Gauduchon Hermitian connections and Dirac operators Boll. Un. Mat. Ital. B (7) 11 Suppl. 2 1997 257-288
26. G.W. Gibbons H. Lü C.N. Pope K.S. Stelle Supersymmetric domain walls from metrics of special holonomy Nucl. Phys. B 623 1-2 2002 3-46
27. G.W. Gibbons G. Papadopoulos K.S. Stelle HKT and OKT geometries on soliton black hole moduli spaces Nucl. Phys. B 508 3 1997 623-658
28. G. Grantcharov Y.S. Poon Geometry of hyper-Kähler connections with torsion Commun. Math. Phys. 213 1 2000 19-37
29. A. Gray L.M. Hervella The sixteen classes of almost Hermitian manifolds and their linear invariants Ann. Mat. Pura Appl. (4) 123 1980 35-58
30. K. Hasegawa Minimal models of nilmanifolds Proc. Am. Math. Soc. 106 1 1989 65-71
31. N.J. Hitchin The geometry of three-forms in six dimensions J. Diff. Geom. 55 3 2000 547-576
32. N.J. Hitchin Stable forms and special metrics, Global differential geometry: The mathematical legacy of Alfred Gray (Bilbao, 2000), Contemp. Math., vol. 288 2001 American Mathematical Society Providence, RI pp. 70-89
33. P.S. Howe A. Opfermann G. Papadopoulos Twistor spaces for QKT manifolds Commun. Math. Phys. 197 3 1998 713-727
34. 2, Spin(7)-heterotic string solitons, December 2003. eprint math.DG/0312094.
35. D.D. Joyce Compact Manifolds with Special Holonomy 2000 Oxford University Press Oxford
36. G. Ketsetzis S. Salamon Complex structures on the Iwasawa manifold Adv. Geom. 4 2004 165-179
37. A.I. Malcev On a class of homogeneous spaces Izvestiya Akad. Nauk. SSSR. Ser. Mat. 13 1949 9-32
38. A.I. Malcev On a class of homogeneous spaces Am. Math. Soc. Translation 1951 39 1951 33
39. 2 -structure Bolletino U.M.I. 10 1996 99-112
40. K. Nomizu On the cohomology of compact homogeneous spaces of nilpotent Lie groups Ann. Math. (2) 59 1954 531-538
41. G. Papadopoulos, KT and HKT geometries in strings and in black hole moduli spaces, January 2002. eprint hep-th/0201111.
42. S.M. Salamon Riemannian geometry and holonomy groups Pitman Research Notes in Mathematics, vol. 201 1989 Longman Harlow
43. S.M. Salamon Complex structures on nilpotent Lie algebras J. Pure Appl. Algebra 157 2-3 2001 311-333
44. D.M. Snow Invariant complex structures on reductive Lie groups J. Reine Angew. Math. 371 1986 191-215
45. A. Strominger Superstrings with torsion Nuclear Phys. B 274 2 1986 253-284