Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A flat two-torus, T^2 that is the torus with Euclidean metric needs to at least be embedded in R^4. If we puncture the torus and leave the Euclidean metric on it as inherited (ignoring the issues of completeness), what ambient space could you embed the punctured torus with Euclidean metric?

share|improve this question
2  
It is a bit strange to call the flat metric on the torus the Euclidean metric... –  Mariano Suárez-Alvarez Feb 14 '11 at 6:01
    
Thinking of $T^2$ as $\mathbb R^2/\mathbb Z^2$, the term Euclidean metric makes some sense. :) –  Grumpy Parsnip Feb 14 '11 at 11:23

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.