Related papers: Holonomy in pseudo-Hermitian geometry

This paper analyses the parabolic geometries generated by a free $n$-distribution in the tangent space of a manifold. It shows that certain holonomy reductions of the associated normal Tractor connections, imply preferred connections with…

We construct homogeneous flat pseudo-Riemannian manifolds with non-abelian fundamental group. In the compact case, all homogeneous flat pseudo-Riemannian manifolds are complete and have abelian linear holonomy group. To the contrary, we…

We demonstrate that all perturbative scale invariant heterotic sigma models with a compact target space $M^D$ are conformally invariant. The proof, presented in detail for up to and including two loops, utilises a geometric analogue of the…

The reductive holonomy algebras for a torsion-free affine connection are analysed, with the goal of establishing which ones can correspond to a Ricci-flat connection with the same properties. Various families of holonomies are eliminated…

We discuss in this paper the conformal geometry of bi-invariant metrics on compact semisimple Lie groups. For this purpose we develop a conformal Cartan calculus adapted to this problem. In particular, we derive an explicit formula for the…

We consider sub-Riemannian spaces admitting an isometry group that is maximal in the sense that any linear isometry between the horizontal tangent spaces is realized by a global isometry. We will show that these spaces have a canonical…

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…

We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skew-symmetric Nijenhuis tensor. We investigate up to what extent the…

In this paper, we study the theory of geodesics with respect to the Tanaka-Webster connection in a pseudo-Hermitian manifold, aiming to generalize some comparison results in Riemannian geometry to the case of pseudo-Hermitian geometry. Some…

In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel…

The notion of a parallelizable distribution has been introduced and investigated. A non-integrable parallelizable distribution carries a natural sub-Riemannian structure. The geometry of this structure has been studied from the bi-viewpoint…

First we survey and explain the strategy of some recent results that construct holomorphic $\text{sl}(2, \mathbb C)$-differential systems over some Riemann surfaces $\Sigma_g$ of genus $g\geq 2$, satisfying the condition that the image of…

We provide a new and simple system of equations for the normal sub-Riemannian geodesics. These use a partial connection that we show is canonically available, given a choice of complement to the distribution. We also describe conditions…

For Cartan geometries admitting automorphisms with isotropies satisfying a particular, loosely dynamical property on their model geometries, we demonstrate the existence of an open subset of the geometry with trivial holonomy. This…

We prove the following monotonicity result for the holonomy group: Given a sequence of metric connections converging in $C^0$ such that all its members have holonomy contained in a closed group $H$, also their limit connection needs to have…

We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit…

A locally metric connection on a smooth manifold $M$ is a torsion-free connection $D$ on $TM$ with compact restricted holonomy group $\mathrm{Hol}_0(D)$. If the holonomy representation of such a connection is irreducible, then $D$ preserves…

The classification problem for holonomy of pseudo-Riemannian manifolds is actual and open. In the present paper, holonomy algebras of Lorentz-K\"ahler manifolds are classified. A simple construction of a metric for each holonomy algebra is…

In this expository article we discuss the relations between Sasakian geometry, reduced holonomy and supersymmetry. It is well known that the Riemannian manifolds other than the round spheres that admit real Killing spinors are precisely…

A locally conformally K\"ahler (lcK) manifold is a complex manifold $(M,J)$ together with a Hermitian metric $g$ which is conformal to a K\"ahler metric in the neighbourhood of each point. In this paper we obtain three classification…