Double vector bundle is roughly a vector bundle over (horizontal) vector bundle.
Vector bundle is a supermanifold in a nature way (non-nature on the other way around).
My question: is a double vector bundle a vector bundle over the supermanifold corresponding to the horizontal vector bundle in a nature way? I can see this is true for double tangent bundle.
This post imported from StackExchange MathOverflow at 2014-08-10 19:52 (UCT), posted by SE-user Ma Ming