The constant osculating rank of the Wilking manifold

We prove that the osculating rank of the Wilking manifold V3 = (SO (3) × SU (3)) / U• (2), endowed with the metric over(g, )1, equals 2. The knowledge of the osculating rank allows us to solve the differential equation of the Jacobi vector fields. These results can be applied to determine the area and the volume of geodesic spheres and balls. To cite this article: E. Macias-Virgos et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008). © 2007 Academie des sciences.