Showing papers on "Frame bundle published in 1973"
TL;DR: In this article, the curvature relations between the bundle space and the base space are studied under the assumption of regularity, and the curvatures of the base and the bundle spaces are analyzed.
Abstract: Under an assumption of regularity a manifold with an f-structure satisfying certain conditions analogous to those of a Kahler structure admits a fibration a s a principal toroidal bundle over a Kaller manifold. In some natural special cases, additional information about the bundle spaceis obtained. Finally, curvature relations between the bundle space and the base space are studied.
44 citations
TL;DR: In this paper, it was shown that Schmidt's b-boundary can be analyzed using a submanifold of the tangent bundle, rather than the principal bundle or the bundle of orthogonal frames.
Abstract: It is shown that Schmidt'sb-boundary for a spacetime can be analyzed using a submanifold of the tangent bundle, rather than the principal bundle or the bundle of orthogonal frames.
13 citations
01 Jan 1973
TL;DR: In this article, the existence of a periodic orbit when certain integrals of such functions arc all 0 or all 0 was proved for 2-dimensional structurally stable differential systems on Riemann manifolds.
Abstract: A C~q differential system S, q≧1, on a compact C~∞ Riemann manifold M~n induces naturally a 1-parameter differentiable transformation group on the tangent bundle of-M~n. A view-point is that the ergodie properties of this transformation group will determine in part the topological structure of the phase portrait of S over M~n. Accordingly, we have previously given the functions ω_k(γ) defined on the bundle of orthonormal l-frames of M~n and associated with S; these functions play an important role in our discussion. What we shall present here is a theorem in this scope, which asserts the existence of a periodic orbit when certain integrals of such functions arc all0 or all0. Using results of this sort and known facts on 2-dimensional structurally stable differential systems, a necessary and sufficient condition will be given for a C~2 system on a closed surface to be structurally stable.
11 citations
9 citations
01 May 1973
8 citations
5 citations
01 Mar 1973
TL;DR: In this article, a resolution of a group bundle y, a classifying spectrum for a cohomology functor H*( ; y) (coefficients in y) defined on a category of fibre spaces, is presented.
Abstract: The purpose of this paper is to construct a resolution of a group bundle y, a classifying spectrum for a cohomology functor H*( ; y) (coefficients in y) defined on a category of fibre spaces, and to clarify and note some implications of the close relationship between these two constructions.
TL;DR: The main theorem of as mentioned in this paper states that if the Spivak normal fibration associated to a Poincare complex admits a vector bundle structure, then it is homotopy equivalent to the union of two smooth manifolds.
Abstract: The main theorem states that if the Spivak normal fibration associated to a Poincare complex admits a vector bundle structure, then the Poincare complex is homotopy equivalent to the union of two smooth manifolds with their boundaries identified via a homotopy equivalence. The theorem is applied to the question of existence of smooth structures on Poincare complexes.