42 citations · 347 across the 35 of their papers we have counts for
36 papers
Prolongation and Killing two-tensors
Michael Eastwood, Thomas Leistner
We present a systematic prolongation procedure and its implementation for Killing two-tensors. We use the resulting machinery to elucidate the natural quadratic mapping from Killin…
Holonomy in pseudo-Hermitian geometry
Anton S. Galaev, Thomas Leistner, Felipe Leitner
We study the holonomy that is associated to a sub-Riemannian structure defined on the kernel of a global contact form. This includes the holonomy of Schouten's horizontal connectio…
Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations
Vicente Cortés, Thomas Leistner
A conformal transformation of a semi-Riemannian manifold is essential if there is no conformally equivalent metric for which it is an isometry. For Riemannian manifolds the existen…
The range of a connection and a Calabi operator for Lorentzian locally symmetric spaces
Federico Costanza, Michael Eastwood, Thomas Leistner +1
For semi-Riemannian manifolds of constant sectional curvature, the Calabi operator is a second order linear differential operator that provides local integrability conditions for t…
Conformal transformations of Cahen-Wallach spaces
Thomas Leistner, Stuart Teisseire
We study conformal transformations of indecomposable Lorentzian symmetric spaces of non-constant sectional curvature, the so-called Cahen-Wallach spaces. When a Cahen-Wallach space…
Fundamental regions for non-isometric group actions
Thomas Leistner, Stuart Teisseire
We generalise results about isometric group actions on metric spaces and their fundamental regions to the context of merely continuous group actions. In particular, we obtain resul…
A Calabi operator for Riemannian locally symmetric spaces
Federico Costanza, Michael Eastwood, Thomas Leistner +1
On a Riemannian manifold of constant curvature, the Calabi operator is a second order linear differential operator that provides local integrability conditions for the range of the…
Almost Robinson geometries
Anna Fino, Thomas Leistner, Arman Taghavi-Chabert
We investigate the geometry of almost Robinson manifolds, Lorentzian analogues of almost Hermitian manifolds, defined by Nurowski and Trautman as Lorentzian manifolds of even dimen…
Optical geometries
Anna Fino, Thomas Leistner, Arman Taghavi-Chabert
We study the notion of optical geometry, defined to be a Lorentzian manifold equipped with a null line distribution, from the perspective of intrinsic torsion. This is an instance…
Semi-Riemannian cones
Thomas Leistner
Due to a result by Gallot a Riemannian cone over a complete Riemannian manifold is either flat or has an irreducible holonomy representation. This is false in general for indefinit…
Geometry and holonomy of indecomposable cones
Dmitri Alekseevsky, Vicente Cortés, Thomas Leistner
We study the geometry and holonomy of semi-Riemannian, time-like metric cones that are indecomposable, i.e., which do not admit a local decomposition into a semi-Riemannian product…
Conformal properties of indefinite bi-invariant metrics
Kelli Francis-Staite, Thomas Leistner
An indecomposable Lie group with Riemannian bi-invariant metric is always simple and hence Einstein. For indefinite metrics this is no longer true, not even for simple Lie groups.…
Invariant prolongation of the Killing tensor equation
A. Rod Gover, Thomas Leistner
The Killing tensor equation is a first order differential equation on symmetric covariant tensors that generalises to higher rank the usual Killing vector equation on Riemannian ma…
Hyperbolic evolution equations, Lorentzian holonomy, and Riemannian generalised Killing spinors
Thomas Leistner, Andree Lischewski
We prove that the Cauchy problem for parallel null vector fields on smooth Lorentzian manifolds is well posed. The proof is based on the derivation and analysis of suitable hyperbo…
Conformal Walker metrics and linear Fefferman-Graham equations
Ian M Anderson, Thomas Leistner, Andree Lischewski +1
The conformal Fefferman-Graham ambient metric construction is one of the most fundamental constructions in conformal geometry. It embeds a manifold with a conformal structure into…
New relations between -geometries in dimensions 5 and 7
Thomas Leistner, Pawel Nurowski, Katja Sagerschnig
There are two well-known parabolic split -geometries in dimension five, -distributions and -contact structures. Here we link these two geometries with yet anothe…
The ambient obstruction tensor and conformal holonomy
Thomas Leistner, Andree Lischewski
For a conformal manifold, we describe a new relation between the ambient obstruction tensor of Fefferman and Graham and the holonomy of the normal conformal Cartan connection. This…
Explicit ambient metrics and holonomy
Ian M. Anderson, Thomas Leistner, Pawel Nurowski
We present three large classes of examples of conformal structures for which the equations for the Fefferman-Graham ambient metric to be Ricci-flat are linear PDEs, which we solve…
Locally homogeneous pp-waves
Wolfgang Globke, Thomas Leistner
We show that every n-dimensional locally homogeneous pp-wave is a plane wave, provided it is indecomposable and its curvature operator, when acting on -forms, has rank greater t…
Cauchy problems for Lorentzian manifolds with special holonomy
Helga Baum, Thomas Leistner, Andree Lischewski
On a Lorentzian manifold the existence of a parallel null vector field implies certain constraint conditions on the induced Riemannian geometry of a space-like hypersurface. We wil…
Completeness of compact Lorentzian manifolds with Abelian holonomy
Thomas Leistner, Daniel Schliebner
We address the problem of finding conditions under which a compact Lorentzian manifold is geodesically complete, a property, which always holds for compact Riemannian manifolds. It…
Conformal holonomy, symmetric spaces, and skew symmetric torsion
Jesse Alt, Antonio J. Di Scala, Thomas Leistner
We consider the question: can the isotropy representation of an irreducible pseudo-Riemannian symmetric space be realized as a conformal holonomy group? Using recent results of Cap…
On the full holonomy group of special Lorentzian manifolds
Helga Baum, Kordian Lärz, Thomas Leistner
We study the full holonomy group of Lorentzian manifolds with a parallel null line bundle. We prove several results that are based on the classification of the restricted holonomy…
Conformal pure radiation with parallel rays
Thomas Leistner, Pawel Nurowski
We define pure radiation metrics with parallel rays to be n-dimensional pseudo-Riemannian metrics that admit a parallel null line bundle K and whose Ricci tensor vanishes on vector…