62 research outputs found
Parallel spinors and holonomy groups on pseudo-Riemannian spinmanifolds
We describe the possible holonomy groups of simply connected irreducible
non-locally symmetric pseudo-Riemannian spin manifolds which admit parallel
spinors.Comment: Latex2.09, 18 page
Local Type I Metrics with Holonomy in
By [arXiv:1604.00528], a list of possible holonomy algebras for
pseudo-Riemannian manifolds with an indecomposable torsion free -structure is known. Here indecomposability means that the standard
representation of the algebra on does not leave invariant
any proper non-degenerate subspace. The dimension of the socle of this
representation is called the type of the Lie algebra. It is equal to one, two
or three. In the present paper, we use Cartan's theory of exterior differential
systems to show that all Lie algebras of Type I from the list in
[arXiv:1604.00528] can indeed be realised as the holonomy of a local metric.
All these Lie algebras are contained in the maximal parabolic subalgebra
that stabilises one isotropic line of . In
particular, we realise by a local metric
Spectra of sub-Dirac operators on certain nilmanifolds
We study sub-Dirac operators that are associated with left-invariant
bracket-generating sub-Riemannian structures on compact quotients of nilpotent
semi-direct products . We will prove that
these operators admit an -basis of eigenfunctions. Explicit examples show
that the spectrum of these operators can be non-discrete and that eigenvalues
may have infinite multiplicity
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