• DOI:10.4310/AJM.2003.V7.N1.A4
• Corpus ID: 13936533

Deformations of generalized calibrations and compact non-Kähler manifolds with vanishing first Chern class

@article{Gutowski2002DeformationsOG,
  title={Deformations of generalized calibrations and compact non-K{\"a}hler manifolds with vanishing first Chern class},
  author={J B Gutowski and Stefan Ivanov and Georgios Papadopoulos},
  journal={Asian Journal of Mathematics},
  year={2002},
  volume={7},
  pages={39-80}
}

• J. Gutowski, S. Ivanov, G. Papadopoulos
• Published 1 May 2002
• Mathematics
• Asian Journal of Mathematics

We investigate the deformation theory of a class of generalized calibrations in Riemannian manifolds for which the tangent bundle has reduced structure group U(n), SU(n), G_2 and Spin(7). For this we use the property of the associated calibration form to be parallel with respect to a metric connection which may have non-vanishing torsion. In all these cases, we find that if there is a moduli space, then it is finite dimensional.
We present various examples of generalized calibrations that include almost hermitian manifolds with structure group U(n) or SU(n), nearly parallel G_2 manifolds and group manifolds. We find that some Hopf fibrations are deformation families of generalized calibrations. In addition, we give sufficient conditions for a hermitian manifold (M,g,J) to admit Chern and Bismut connections with holonomy contained in SU(n). In particular we show that any connected sum of $k \geq 3$ copies of $S^3 \times S^3$ admits a hermitian structure for which the restricted holonomy of a Bismut connection is contained in SU(3).