Showing papers on "Unit tangent bundle published in 1983"

Tangent bundle geometry Lagrangian dynamics

Abstract: Various aspects of the differential geometry of the tangent bundle of a differentiable manifold are examined, and the results applied to time-independent Lagrangian dynamics. It is shown that a certain type (1, 1) tensor field which is part of the intrinsic geometry of a tangent bundle, being a tensorial equivalent of the projection map of tangent vectors, plays a role in Lagrangian theory scarcely less important than that of the canonical one-form on a cotangent bundle in Hamiltonian theory. Recent results in Lagrangian theory are interpreted from this new viewpoint.

Geometry of tangent bundles and spaces over algebras

Abstract: Papers from the last eight-nine years are considered, which relate to the geometry of tangent bundles and spaces over algebras. Special attention is given to those questions of the geometry of tangent bundles, which are connected with the concept of “close points” in the sense of A. Weil, and hence also with structures, defined by local algebras.

Lifts of tensor fields to the frame bundle

Abstract: LetM be a differentiable manifold,T M its tangent bundle andFM its frame bundle. The theory of lifts toT M of tensor fields onM has been extensively studied by many authors. In this paper, a similar theory for the frame bundle is developed by introducing the complete, horizontal and diagonal lifts toFM of tensor fields onM, with the aim of making this study as closely comparable with that forT M as possible.

On the tangent bundle of a flag variety

Abstract: In this paper we give a description of the tangent bundle of a flag variety in terms of the universal bundles on such a variety (Theorem 2.1).