Showing papers on "Unit tangent bundle published in 1967"

Prolongations of tensor fields and connections to tangent bundles III

Abstract: In our previous paper [3] we introduced the notion of complete lift of an afl\"ine connection. Let M be a manifold T(M) its tangent bundle space. Then every affine connection 17 of M induces in a natural manner an affine connection, called the complete lift 17c of 17, of the manifold T(M). We shall show in this paper that the linear holonomy group L(I7c) of the connection UC coincides with the tangent group T(~(V)) of the linear holonomy group P(P) of the connection 17, i. e., ~(Pc) = T(P(G)).

The immersion of manifolds

Abstract: 1. M. Hirsch [3] has shown that the immersion problem for manifolds is just a cross section problem for the stable normal bundle. Our object here is to find conditions under which sections of the tangent bundle will imply sections in the normal bundle (and conversely). First we need some notation. Given an integer /, let j(t) be the maximum integer such that the 2*-f old Whitney sum of the Hopf bundle over RP^~ is trivial. If £ is a stable bundle, let gd(£) denote the geometric dimension of £.

A note on tangent bundles

Abstract: The tangent bundle of a differentiable manifold is an important invariant of a differentiable structure. It is determined neither by the topological structure nor by the homotopy type of a manifold. But in some cases tangent bundles depend only on the homotopy types of manifolds.