553 research outputs found
The intrinsic torsion of SU(3) and G_2 structures
We analyse the relationship between the components of the intrinsic torsion
of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold.
Various examples illustrate the type of SU(3) structure that can arise as a
reduction of a metric with holonomy G_2.Comment: Proc. conf. Differential Geometry Valencia 200
Half-flat structures on products of three-dimensional Lie groups
We classify six-dimensional Lie groups which admit a left-invariant half-flat
SU(3)-structure and which split in a direct product of three-dimensional
factors. Moreover, a complete list of those direct products is obtained which
admit a left-invariant half-flat SU(3)-structure such that the
three-dimensional factors are orthogonal. Similar classification results are
proved for left-invariant half-flat SL(3,R)-structures on direct products with
either definite and orthogonal or isotropic factors.Comment: 19 page
SO(3)-Structures on 8-manifolds
We study Riemannian 8-manifolds with an infinitesimal action of SO(3) by
which each tangent space breaks into irreducible spaces of dimensions 3 and 5.
The relationship with quaternionic, almost product- and PSU-geometry is
thoroughly explained using representation-theoretical arguments.Comment: 19 pages, 2 figure
A landscape of non-supersymmetric AdS vacua on coset manifolds
We construct new families of non-supersymmetric sourceless type IIA AdS4
vacua on those coset manifolds that also admit supersymmetric solutions. We
investigate the spectrum of left-invariant modes and find that most, but not
all, of the vacua are stable under these fluctuations. Generically, there are
also no massless moduli.Comment: 20 pages, 11 figures, v2: added some clarifications, references, v3:
corrections addressing comments refere
Complex homothetic foliations on K\"ahler manifolds
We obtain a local classification of complex homothetic foliations on Kaehler
manifolds by complex curves. This is used to construct almost Kaehler,
Ricci-flat metrics subject to additional curvature properties.Comment: Final version, up to typos. To appear in BLM
Systems of symplectic forms on four-manifolds
We study almost Hermitian 4-manifolds with holonomy algebra, for the
canonical Hermitian connection, of dimension at most one. We show how
Riemannian 4-manifolds admitting five orthonormal symplectic forms fit therein
and classify them. In this set-up we also fully describe almost Kaehler
4-manifolds.Comment: Final version, to appear in Annali di SNS.added thm. 5.
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