**SMS scnews item created by Stephan Tillmann at Tue 2 Sep 2014 1617**

Type: Seminar

Distribution: World

Expiry: 2 Dec 2014

**Calendar1: 3 Sep 2014 1100-1200**

**CalLoc1: Carslaw 535A**

Auth: tillmann@p710.pc (assumed)

### Geometry-Topology-Analysis Seminar

# Flat Tori of Finite Type in S3

### Alan McCarthy

##
Flat Tori of Finite Type in \(S^3\)

Alan McCarthy (UNSW)

Abstract

A torus in the three sphere (\(S^3\)) is said to be flat if it's Gaussian
curvature is identically zero. Flat surfaces in \(S^3\) are of particular
interest as they are the only complete surfaces in \(S^3\) with constant
curvature that are not spheres. In this talk I will explain in more detail
what I mean by 'flat', why the Gaussian curvature of a surface in \(S^3\) is not
exactly the same as the Guassian curvature of a surface in \(R^3\). A summary
will be given of the classification of flat tori in \(S^3\) in terms of their
asymptotic curves due to Kitagawa, Bianchi and Spivak. I will also give a
brief overview of my research into finite type flat tori and will explain
why these objects are of interest.

Please joint us for lunch after the talk!

Cheers,

Stephan