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)

# Flat Tori of Finite Type in S3

## 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

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