No Access
GENERALIZED G2-MANIFOLDS AND SU(3)-STRUCTURES
Abstract
We construct a family of compact 7-dimensional manifolds endowed with a weakly integrable generalized G2-structure with respect to a closed and non-zero 3-form. We relate the previous structures with SU(3)-structures in dimension 7. Moreover, we investigate which types of SU(3)-structures on a 6-dimensional manifold N give rise to a strongly integrable generalized G2-structure with respect to a non-zero 3-form on the product N × S1.
AMSC: 53C10, 53C25, 83E50
References
- J. Geom. Phys. 57, 1125 (2007), DOI: 10.1016/j.geomphys.2006.09.007. Crossref, ISI, Google Scholar
- Monatsh. Math. 148, 29 (2006), DOI: 10.1007/s00605-005-0343-y. Crossref, ISI, Google Scholar
- J. Geom. Phys. 55, 450 (2005). Crossref, ISI, Google Scholar
- Math. Z. 252, 825 (2006), DOI: 10.1007/s00209-005-0885-7. Crossref, ISI, Google Scholar
S. Chiossi and S. Salamon , Differential Geometry (World Scientific Publishing, River Edge, NJ, 2002) pp. 115–133. Google Scholar- Trans. AMS 359, 5319 (2007), DOI: 10.1090/S0002-9947-07-04307-3. Crossref, ISI, Google Scholar
- Quart. J. Math. 58, 297 (2007), DOI: 10.1093/qmath/ham013. Crossref, ISI, Google Scholar
- Int. J. Math. 17, 921 (2006). Link, ISI, Google Scholar
- J. Differential Geom. 26, 367 (1987). Crossref, ISI, Google Scholar
- Commun. Math. Phys. 247, 421 (2004), DOI: 10.1007/s00220-004-1066-y. Crossref, ISI, Google Scholar
- Acta Math. 148, 47 (1982), DOI: 10.1007/BF02392726. Crossref, ISI, Google Scholar
- , Global Differential Geometry: The Mathematical Legacy of Alfred Gray,
Contemporary Mathematics 288, eds.M. Fernández and J. A. Wolf (American Mathematics Society, Providence, RI, 2001) pp. 70–89. Crossref, Google Scholar - Quart. J. Math. 54, 281 (2003), DOI: 10.1093/qmath/hag025. Crossref, ISI, Google Scholar
- J. High Energy Phys. 3, 15 (2005). Google Scholar
- J. Differential Geom. 10, 85 (1975). Crossref, Google Scholar
- Osaka J. Math. 45, 127 (2008), math.DG/0612232. ISI, Google Scholar
- Commun. Math. Phys. 265, 275 (2006), DOI: 10.1007/s00220-006-0011-7. Crossref, ISI, Google Scholar
- F. Witt, Closed forms and special metrics, thesis, University of Oxford (2004), e-print math.DG/0502443 . Google Scholar
