XXVIII Workshop on Geometric Methods in Physics 28.06-04.07.2009

Rotkiewicz Mikolaj

Higher vector bundles

It is a simple natural condition assuring that an action of the
multiplicative monoid of non-negative reals on a manifold $F$
comes from homoteties of a vector bundle structure on $F$. We use it to show that double (or higher)
vector bundles
present in the literature can be equivalently defined as manifolds
with a family of commuting Euler vector fields. The canonical examples are (iterated)
tangent and cotangent bundles $TE$, $T^*E$, $TT^*E$, etc., of a vector bundle $E$.