Difference between revisions of "Curvature of direct sum of connections equals direct sum of curvatures"
(Created page with '==Statement== Suppose <math>E,E'</math> are vector bundles over a differential manifold <math>M</math>. Suppose <math>\nabla,\nabla'</math> are connections on <math>…')
Revision as of 22:19, 24 July 2009
Suppose are vector bundles over a differential manifold . Suppose are connections on respectively. Let denote the Riemann curvature tensor of and denote that Riemann curvature tensor of . Then if is the direct sum of vector bundles, is the direct sum of connections, and is its Riemann curvature tensor, we have: