We extend the Gallot-Tanno theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over a manifold admits a parallel symmetric (0, 2)-tensor then it is Riemannian. Applications of this result to the existence of metrics with distinct Levi-Civita connections but having the same unparametrized geodesics and to the projective Obata conjecture are given. We also apply our result to show that the holonomy group of a closed (O( p + 1, q), S p,q )-manifold does not preserve any nondegenerate splitting of R p+1,q .

We investigated visuo-manual pursuit tracking in 10 adult subjects. The main features of the experi ments were as follows: (a) The targets to be pursued were planar (two-dimensional) trajectories. (b) Targets were based on actual human hand movements. A set of five different extemporaneous movements (scribbles) were rear-projected on a digitizing table with their original timescale. (c) Targets were presented both as originally recorded (Condition N) and after a numerical manipulation that made the tangential velocity constant throughout the motion (Condition T). After a set of de scriptors of the performance suitable for the two-dimensional case was introduced, individual perfor mances were analyzed to characterize both the features common to all subjects and the idiosyncratic differences. The main results of the study were as follows: (a) Performances are extremely consistent across repetitions. Differences among subjects are mostly confined to the value of the descriptors. (b) The single most characteristic descriptor is the instantaneous delay between target and pursuit. The position error depends jointly on this delay and the instantaneous target velocity. (c) The operat ing strategy is significantly modified in Condition T. (d) A simple formal scheme based on the notion of a delayed velocity feedback accounts quite accurately for the experimental results. This is in contrast with most classical models of pursuit tracking.

ABSTRACT. In a previous article, we reported an investigation of visuomanual pursuit tracking of unpredictable two-dimensional targets. This article extends the study to the tracking of predictable stimuli. In both investigations, the target trajec tory was elliptical. The experimental factors we vari ed were the orientation of the

No abstract

Abstract