# Curvature of direct sum of connections equals direct sum of curvatures

## Statement

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:

.