New Publications:
Helga Baum, Kordian Lärz and Thomas Leistner : On the full
holonomy
group of special Lorentzian manifolds. [pdf]
arXiv:1204.5657v2
(2012)
Abstract: 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 restrictad holonomy groups of such manifolds and provide a
construction method for manifolds with disconnected holonomy
which starts from a Riemannian manifold and a properly discontinouous
group of isometries. Most of our examples are quotients of pp-waves
with disconnected holonomy and without parallel spinor field.
Furthermore, we classify the full holonomy group of solvable Lorentzian
symmetric spaces and of Lorentzian manifolds with parallel spinor.
Finally, we construct examples of globaly hyperbolic manifolds with
complete spacelike Cauchy surfaces, disconnected full holonomy and
parallel spinor.
Helga
Baum: Holonomy groups of Lorentzian manifolds - a status report.
In: Global Differential Geometry,
eds. C.Bär, J. Lohkamp and M. Schwarz,. p.163-200, Springer
Proceedings in Mathematics Vol. 17, Springer-Verlag, 2012. [pdf]
Helga
Baum: The conformal analog of Calabi-Yau manifolds. [ps]
[pdf]
In: Handbook of Pseudo-Riemannian Geometry and
Supersymmerty, IRMA Lectures in Mathematics and Theoretical
Physics, Vol. 40, eds. V. Cortés, Publishing House of the
EMS, 2010.
Abstract:
This survey intends to introduce the reader to
holonomy theory of Cartan connections. Special attention is given to
the normal conformal Cartan connection, uniquely defined for a class
of conformally equivalent metrics, and to its holonomy group -
the 'conformal holonomy group'. We explain the relation between
conformal holonomy group and existence of Einstein metrics in the
conformal class as well as the relation between conformal holonomy
group and existence of conformal Killing spinors. In particular, we
describe Lorentzian manifolds with conformal holonomy group in SU(1,m),
which can be viewed as conformal analog of Calabi-Yau manifolds. Such
Lorentzian metrics, known as Fefferman metrics, appear on S1-bundles
over
strictly
pseudoconvex
CR spin manifolds.
Helga
Baum
and Andreas Juhl: Conformal Differential Geometry. Q-curvatrue
and
conformal holonomy.
Oberwolfach Seminars, Vol. 40, Birkhäuser-Verlag, 2010.
Flyer
Helga
Baum: Eichfeldtheorie.
Springer-Verlag
2009 Flyer
Dmitri
Alekseevsky and Helga Baum
(eds): Recent Developments in
Pseudo-Riemannian Geometry
ESI Lecture Series in Mathematics and
Physics, EMS Publishing House 2008, 537 pp. Flyer
Helga
Baum
and
Olaf
Müller:
Codazzi spinors and globally
hyperbolic
Lorentzian manifolds with special holonomy.
Mathematische Zeitschrift 258
(2008), 185-211. [pdf]
Abstract: In
this
paper
we prove that any Lorentzian holonomy group of the form G xs
Rn-2 , where G is trivial or a product of groups SU(k),
Sp(l), G2 or Spin(7) can be realized by a globally
hyperbolic Lorentzian manifold with geodesically
complete Cauchy
surfaces. For that aim we describe the
structure of Riemannian manifolds with
Codazzi spinors to invertible Codazzi tensors.
Helga
Baum: Conformal Killing spinors
and the holonomy problem in
Lorentzian
geometry - a survey of new results.
In: Symmetries and Overdetermined
Systems of Partial Differential Equations, eds. M. Eastwood, W. Miller,
251--264, IMA Volumes in Mathematics, Springer 2008.
[ps]
[pdf]
Abstract: This
paper is a
survey of recent results about conformal Killing spinors in Lorentzian
geometry based on a lecture given during the Summer Program Symmetries and Overdetermined Systems of
Partial Differential Equations at IMA, Minnesota, 17.07.06
-04.08.06. In particular, we will focus on a special class of
geometries admitting conformal Killing spinors - on Brinkmann spaces
with parallel spinors. We will discuss their holonomy groups and the
global realizability as globally hyperbolic spaces.
All
Publications
Last Modification: 16.05.2012
