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Deformations of generalized calibrations and compact non-Kähler manifolds with vanishing first Chern class
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gutowski, Jan Ivanov, Stefan Papadopoulos, George |
| Copyright Year | 2002 |
| Abstract | 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), G2 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 G2 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 compact complex 3-fold with holomorphically trivial canonical bundle admits a hermitian structure for which the restricted holonomy of a Bismut connection is contained in SU(3). |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0205012v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Calibration Contain (action) Hopf bifurcation Hospital admission Torsion (gastropod) manifold |
| Content Type | Text |
| Resource Type | Article |
