DIFFERENTIAL GEOMETRY WORKSHOPat LUND 2014in connection withTHE 10TH DIFFERENTIAL GEOMETRY DAY

ABSTRACTS

Thursday the 15th of May 2014

Martin Svensson
(SDU Odense, DK)

Timelike CMC surfaces and the geometric Cauchy problem

I will describe the loop group construction of timelike CMC surfaces in
Minkowski 3-space. I will show how to use this construction to solve the
associated geometric Cauchy problem: given a curve and a vector field along
this curve, find a timelike CMC surface that contains this curve and is
everywhere tangent to the given vector field. Finally, I will discuss the
surface singularities that arise when the boundary of the big Birkhoff
cell is approached, and how to construct surfaces with prescribed
singularities. The talk is based on joint work with David Brander (DTU).

Sigmundur Gudmundsson
(Lund University, SE)

Harmonic Morphisms from Homogeneous Spaces - Some Existence Theory

Harmonic morphisms $\phi:(M,g)\to(N,h)$ between Riemannian manifolds are
solutions to over-determined non-linear systems of partial differential
equations determined by the geometric data of the manifolds involved.
For this reason, harmonic morphisms are difficult to find and have no
general existence theory, not even locally.  In this talk we discuss
recent existence results for complex-valued harmonic morphisms from
various Riemannian homogeneous spaces, in particular, Lie groups and
symmetric spaces.

Marina Ville
(University of Tours, FR)

Harmonic morphisms from 4-manifolds to 2-surfaces

We investigate the singular points of a harmonic morphism F from a Riemannian
4-manifold M to a surface. As an illustration we will  recall a construction
by Jean-Marie Burel on S^4. Then we will show that under extra assumptions
(an isolated singular point or a compact M), F is holomorphic near the singular
point w.r.t. a local almost complex structure on an open set of M. Given our
knowledge of J-holomorphic curves, this gives us a good description of the
singular points. (joint work with Ali Makki)

Eric Loubeau
(University of Brest, FR)

Surfaces in spheres: biharmonic and CMC

CMC surfaces in spheres are investigated under the extra condition of
biharmonicity. From the work of Miyata, especially in the flat case, we
give a complete description of such immersions and show that for any
$h\in (0,1)$ there exist CMC planes and cylinders in $S^5$ with
$|H|=h$, while a necessary and sufficient condition on $h$ is found for
the existence of CMC tori in $S^5$.

Friday the 16th of May 2014

Jonas Nordström
(Lund University, SE)

Harmonic morphisms from Riemannian Lie groups

(University of Bucharest, RO)

Shear-free fluids and p-harmonic morphisms. A local classification

The Penrose transform in quaternionic geometry

I shall describe the Penrose transform, in the setting of quaternionic
geometry, with a view towards harmonic' morphisms (work in progress).

Steen Markvorsen
(Danish Technical University, DK)

Fields of Pointed Ovaloids - A Geometric Analysis

In a given chart the r-distance spheres of a Riemannian manifold are
- for a sufficiently small r -  represented by a pointed field of strongly
convex ovaloids. In the talk we will motivate and discuss the natural
questions concerning firstly the reconstruction of the metric from the
ovaloid field and secondly the extension of the ovaloid field to any other
`