Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Table of Contents - 1988 - Volume 109, Issue 3-4  

Research Article

Integrable spreads and spaces of constant curvature

H. R. Farrana1 and S. A. Robertsona2

a1 Department of Mathematics, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait

a2 Department of Mathematics, University of Southampton, Southampton SO9 5NH, U.K.

Synopsis

This paper is a continuation of [2], where we introduced the notion of global k-spreads on manifolds. Here we show that the space of all k-spreads on a manifold has the structure of an affine space, modelled on the vector space of sections of a certain vector bundle. We give some sufficient conditions for a manifold admitting an integrable k-spread to be a space of constant curvature and answer one of the questions raised in [2].

(Received August 01 1986)

(Revised September 11 1987)