Hyperkaehler manifolds with torsion, supersymmetry and Hodge theory
| dc.creator | Verbitsky, Misha | |
| dc.date | 2001-12-20 | |
| dc.date | 2002-01-04 | |
| dc.date.accessioned | 2026-07-07T04:45:23Z | |
| dc.date.available | 2026-07-07T04:45:23Z | |
| dc.description | Let M be a hypercomplex Hermitian manifold, (M,I) the same manifold considered as a complex Hermitian with a complex structure I induced by the quaternions. The standard linear-algebraic construction produces a canonical nowhere degenerate (2,0)-form on (M,I). It is well known that M is hyperkaehler if and only if the form Ωis closed with respect to the de Rham differential. The M is called HKT (hyperkaehler with torsion) if this form is closed with respect to the Dolbeault differential (this condition is weaker. Conjecturally, all compact hypercomplex manifolds admit an HKT-metrics. We exploit a remarkable analogy between the de Rham DG-algebra of a Kaehler manifold and the Dolbeault DG-algebra of an HKT-manifold. The supersymmetry of a Kaehler manifold is given by an action of an 8-dimensional Lie superalgebra on its de Rham algebra, containing the Lefschetz SL(2)-triple, the Laplacian and the de Rham differential. We establish the action of this superalgebra on the Dolbeault DG-algebra of an HKT-manifold. This is used to construct a canonical Lefschetz-type SL(2)-action on the space of harmonic spinors of M. | |
| dc.description | 47 pages, more reference and history added | |
| dc.identifier | https://arxiv.org/abs/math/0112215 | |
| dc.identifier | http://arxiv.org/abs/math/0112215 | |
| dc.identifier | Asian J. Math. Vol. 6, No. 4, pp. 679-712 (2002) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62933 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.title | Hyperkaehler manifolds with torsion, supersymmetry and Hodge theory | |
| dc.type | text |