Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I am looking for examples of 2- and 3-dimensional flat spin manifolds with Euclidean and Lorentzian signatures, which admit parallel spinors and the dimension of the space of the parallel spinors is equal to 1. At the moment I have examples only for the Lorentzian case:$\mathbb{R}^{1,1}_{*}/(Z_{2})$ (for dimension 2) and $\mathbb{R}^{1,1}_{*}/(Z_{2}) \times \mathbb{R}$ (for dimension 3). Here $\mathbb{R}^{1,1}_{*}$ means $\mathbb{R}^{1,1}\setminus \{(0,0)\}$ and the generator of $Z_2$ acts as $x \mapsto (-x)$. However, I am not sure if it is correct.

share|improve this question
    
Your both examples are correct. –  Vladimir Oct 3 '13 at 12:10

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.