Symmetric bundles and representations of
Lie triple systems
We define symmetric bundles as vector bundles in the category of symmetric spaces;
it is shown that this notion is the geometric analog of the one of a
representation of a Lie triple system.
A symmetric bundle has an underlying reflection space, and
we investigate the corresponding forgetful functor both from the point of
view of differential geometry and from the point of view of representation theory.
This functor is not injective, as is seen
by a Jordan-theoretic construction of ``unusual'' symmetric bundle structures on the tangent bundles
of certain symmetric spaces.
Wolfgang Bertram < bertram@iecn.u-nancy.fr >
Manon Didry < didrym@iecn.u-nancy.fr >