Abstract: Given
-bundles and
with
connections G on X and Ñ on Y and
Riemannian metrics on
V and h on W, we study
immersions inducing
both the given bundle with connection and the given metric. Our study relies on
Nash-Gromov implicit function theorem. We show, for the case when is
the Hopf bundle, that if then
there exists a nonempty open subset in the space of
-pairs on V
which can be induced from on
Keywords and phrases: connections, Nash’s implicit function theorem.
