Arbeitsgruppe Differentialgeometrie
(Prof. Dr. B. Wilking, Prof. Dr. C. Böhm)


Vorträge im Oberseminar Differentialgeometrie, WS 2009/2010

Datum
 Vortragender
 Titel
19.10.2009 Haskins, Mark
(Imperial College, London)



 G2 manifolds, complex 3-folds and associative submanifolds
27.04.2009 Freyn, Walter
(WWU Münster)



 Kac-Moody symmetric spaces       
02.11.2009 Herreros, Pilar
(WWU Münster)		 Closed circles and rigidity of magnetic flow

In general, circles can be defined as curves of constant geodesic curvature.
A magnetic geodesic describes the trajectory of a charged
particle in the presence of a magnetic field. I will introduce this
concepts and how they relate, as well as discuss some boundary
rigidity results in this setting. We will also see how this can be
used to show a rigidity statement regarding closed circles.
09.11.2009 Kapovich, Misha
(University of California)



 Gromov's proof of Stallings' theorem and energy of harmonic functions
16.11.2009 Galaz Garcia, Fernando
(WWU, Münster)
 Low-dimensional nonnegatively curved fixed-point homogeneous manifolds.

Let G be a compact Lie group acting isometrically on a compact Riemannian manifold M with nonempty fixed point set Fix(M;G). We say that M is fixed point homogeneous if G acts transitively on a normal sphere to some component of Fix(M;G). Fixed point homogeneous manifolds with positive sectional curvature have been completely classified.
We will discuss the structure of fi xed point homogeneous Riemannian manifolds with nonnegative curvature and their classification in low dimensions.
23.11.2009 Metzger, Jan
(Universität Freiburg)		 Surfaces of Willmore type in Riemannian manifolds

 In this talk I present recent results on surfaces of
Willmore type in three dimensional Riemannian manifolds. These are
surfaces that are critical for the Willmore energy subject to an area
constraint.  I present an analysis of spherical surfaces of Willmore
type with positive mean curvature in geodesic balls of small
radius. As a result we obtain that such surfaces are well approximated
by geodesic spheres. This enables us to derive necessary conditions
for the existence of such surfaces related to the scalar curvature of
the ambient manifold.
07.12.2009


 Krantz, Tom
(TU Dortmund)		 Torsionsfreie Zusammenhänge mit nicht komplett reduzibler Holonomie
14.12.2009


 Tuschmann, Wilderich
(Christian-Albrechts-Univ.,
Kiel)		 Nonnegative vs. amlost nonnegative curvature operator
04.01.2010

 Matveev, Vladimir
(Friedrich-Schiller-Univ., Jena)

"Projective transformation of pseudo-Riemannian manifolds: rigidity of Einstein manifolds and Lichnerowicz conjecture"

Abstract:
Two metrics g and g' are geodesically equivalent, if every g-geodesic, after the appro- priate reparameterisation, is a g'-geodesic. In the present talk, which is in particular  based on recent joint paper with Kiosak (http://xxx.lanl.gov/abs/0806.3169),

I will consider geodesic equivalence of pseudo-Riemannian metrics such that the metric g is Einstein.
The main result of the talk gives a complete answer to a question posed by Weyl and Petrov and is Theorem:
Let g is an Einstein metric on a 4-dimensional M. If g' is geodesically equivalent to g, then it is affine equivalent to g, i.e., g and g' have the same Levi-Civita connection.

The proof of this theorem is nontrivial and contains new ideas. The rest of the talk is devoted to application of these new ideas to different questions in the Riemannian and pseudo-Riemannian geometry. The big plan is to prove the conformal rigidity of Einstein metrics,  nonexistence of  decomposable cones over closed pseudo-Riemannian manifolds,   to prove an important partial case of the projective Lichnerowicz conjecture, and to solve a classical problem explicitly stated by Sophus Lie, but I will be happy if I manage to  fulfill only part of these.
11.01.2010

 Leschke, Katrin
(University of Leicester )

"The spectral curve of a conformal torus"

 Classically, a spectral curve can be associated to tori which are given by a harmonicity condition, such as constant mean curvature tori or Willmore tori. The harmonicity allows to introduce a spectral parameter  and one obtains an associated family of flat connections: the spectral curve is then essentially given by the eigenvalues of the holonomies of the flat connections.

Recently, a more general notion of a spectral curve has been introduced for any conformally immersed torus in the 4-sphere. We will give a geometric interpretation of the spectral curve in terms of Darboux transforms and will illustrate the construction in the case of a constant mean curvature torus.
18.01.2010
 Walsh, Mark
(WWU Münster) 		Isotopy and concordance in positive scalar curvature
25.01.2010
 Wilking Burkhard
(WWU Münster)
  A Lie theoretic approach to Ricci flow invariant curvature conditions
01.02.2010 Kath, Ines
(Ernst-Moritz-Arndt-Univ.,
Greifswald)

Lorentzian extrinsic symmetric spaces.

Abstract:

A non-degenerate submanifold  of a pseudo-Euclidean space is called an extrinsic symmetric space if it is invariant under the reflection at each of its normal spaces. Similar to usual symmetric spaces extrinsic symmetric 

spaces  can be characterised by curvature. They are exactly those connected complete submanifolds whose second fundamental form is parallel. We describe extrinsic symmetric spaces by their associated infinitesimal objects. We sketch a structure theory for these algebraic objects. As an application we classify all Lorentzian extrinsic symmetric spaces in arbitrary pseudo-Euclidean spaces.



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Letzte Änderung 12.01.2010