most recent 30 from http://mathoverflow.net 2013-06-18T22:39:10Z http://mathoverflow.net/feeds/question/62886 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/62886/horizontal-distribution-of-principal-g-bundle Hu Yi Chen 2011-04-25T03:10:08Z 2011-04-25T03:10:08Z

<p>If we consider $S^{2n-1}$->$\mathbb{CP}^{n-1}$ as a $S^1$ principal bundle, and given a connection 1-form as $C=\frac{1}{2\pi}\Sigma_i(x_i dx_i-y_i dy_i)$ (where $(x_1,y_1,...,x_{2n},y_{2n})$ are coordinates on $S^{2n-1}$). I think the horizontal distribution is the set of points $(x_1,y_1,...,x_{2n},y_{2n})$ and any real multiply of that point, which is just $\mathbb{RP}^{2n-2}$, is that right?</p>