Showing papers on "Distribution (differential geometry) published in 1984"
TL;DR: In this paper, the distribution of 2-plane elements on which infinitesimal parallel displacement of isovectors yields identity was studied and an algebraic and differential classification was given.
Abstract: We study the distribution of 2‐plane elements on which infinitesimal parallel displacement of isovectors yields identity. This yields to an algebraic and differential classification and, in the generic case, to a quasimetric naturally associated with the field.
108 citations
TL;DR: In this article, the authors derived necessary conditions that a real analytic k-dimensional distibution on M have a local basis which generates a nilpotent subalgebra of V(M) and used Darboux's theorem to give a computable test for an n − 1-dimensional distribution.
49 citations
TL;DR: In this article, a universal version of Raychaudhuri's equation for a geodesic local vector field on a space-time manifold has been shown to be universal.
Abstract: The metric connection on a space-time manifoldM defines on its tangent bundleTM a distribution of subspaces complementary to the vertical subspaces and therefore called horizontal. We give a formula for the Lie derivative with respect to the geodesic spray of the tensor field onTM which defines projection onto the vertical subspace along the horizontal subspace; and we show that this formula is a universal version of the equation, for a geodesic local vector field onM, whose trace is Raychaudhuri's equation.
14 citations