ON THE STRICTLY PARALLEL SUBBUNDLES OF VECTOR BUNDLES

Abstract

In this paper are considered four propositions about strictly parallel subbundles of vector bundles. In propositions 1 and 2 are generalized some results of Walker [1] and Wong [2] in case of an arbitrary vector bundle, instead of tangent bundle. Proposition 3 generalizes one Wong’s result [2] in global case. In proposition 4 are given necessary and sufficient conditions for existence of a connection in a vector bundle \(\xi\) such that given \(r\) linearly independent vector fields and \(s\) linearly independent 1-forms in \(\xi\) are parallel. That condition is given by (3).