Riemannian metrics in fiber spaces. II: The metric of a Grassmann foliation (Q677778)

[For part I, see the review in Zbl 0858.53032.] The objective of the present article is to study in detail the Riemannian metric of a Grassmann foliation. It is obtained a coordinate representation of this metric which allows us to compare its restrictions to the vertical fibers with the well-known coordinate expression for the Riemannian metric of the Grassmannian. The main result clarifies the geometrical meaning of the Riemannian metric of the Grassmann foliation in terms of angles and parallel translations in the spirit of what is known of the Sasaki and Mok metrics.