An intrinsic volume functional on almost complex 6-manifolds and nearly Kaehler geometry
| dc.creator | Verbitsky, Misha | |
| dc.date | 2005-07-08 | |
| dc.date | 2007-11-02 | |
| dc.date.accessioned | 2026-07-07T09:31:50Z | |
| dc.date.available | 2026-07-07T09:31:50Z | |
| dc.description | Let $(M,I)$ be an almost complex 6-manifold. The obstruction to integrability of almost complex structure (so-called Nijenhuis tensor) maps a 3-dimensional bundle to a 3-dimensional one. We say that Nijenhuis tensor is non-degenerate if it is an isomorphism. An almost complex manifold is called nearly Kaehler if it admits a Hermitian form $ω$ such that $\nabla(ω)$ is totally antisymmetric, $\nabla$ being the Levi-Civita connection. We show that a nearly Kaehler metric on a given almost complex 6-manifold with non-degenerate Nijenhuis tensor is unique (up to a constant). We interpret the nearly Kaehler property in terms of G_2-geometry and in terms of connections with totally antisymmetric torsion, obtaining a number of equivalent definitions. Further on, we construct an intrinsic diffeomorphism-invariant functional on the space of almost complex structures on $M$, similar to the Hitchin functional, and compute its extrema in the following important case. Consider an almost complex structure $I$ with non-degenerate Nijenhuis tensor, admitting a Hermitian connection with totally antisymmetric torsion. We show that the intrinsic volume functional has an extremum in $I$ if and only if $(M,I)$ is nearly Kaehler. | |
| dc.description | 27 pages, v. 6.1, a few minor errors corrected, reference added | |
| dc.identifier | https://arxiv.org/abs/math/0507179 | |
| dc.identifier | http://arxiv.org/abs/math/0507179 | |
| dc.identifier | Pacific J. of Math., Vol. 235, No. 2 (2008), 323-344 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158600 | |
| dc.subject | Differential Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.title | An intrinsic volume functional on almost complex 6-manifolds and nearly Kaehler geometry | |
| dc.type | text |