Explore the Two-Torus T²: A Visual Guide and Explanation

[waterfall]

Hi, I can't find any picture of a two-torus T² in the net after much searching. Does anyone have a link or can draw what it looks like? Thanks.

 

[Matterwave]

That's just a doughnut...should be the easiest to find on google. Just google torus, it's the standard torus. http://en.wikipedia.org/wiki/Torus

 

[SteveL27]

Here's a picture of the standard embedding of T^2 in R^3.

http://en.wikipedia.org/wiki/File:Randy's_donuts1_edit1.jpg

 

[waterfall]

oh. so it's just a donut.. I was thinking of many dimensional donuts...

if anyone has links to videos which show clearly how complex topologies like 6 dimensional Calabi-Yau can be ricci-flat, pls share it so it can be appreciated visually... thanks.

 

[mathwonk]

The standard embedding of T^2 in R^3 is of course not flat. You need to consider it as a product of circles in R^4 for that.