Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Thomas Mettler
Affiliation:

Universität Frankfurt
Date:

Thu, 13/06/2019 - 16:30 - 17:30 A path geometry on a surface M prescribes an immersed path for every

direction in each tangent space of M. Fixing a Riemannian metric g on M, a

path geometry can be encoded in terms of a real-valued function f on the

unit tangent bundle of (M,g). Requiring the paths to agree with the

geodesics of some connection is equivalent to the condition that the

vertical Fourier expansion of f contains only terms of degree 1 and 3. I

will relate the vanishing of these Fourier modes to (pseudo-)holomorphic

curves and discuss related PDE problems. Joint with Gabriel Paternain.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/3050