Abstract
We prove that the osculating rank of the Wilking manifold V 3 = ( SO ( 3 ) × SU ( 3 ) ) / U • ( 2 ) , endowed with the metric 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. Macías-Virgós et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).
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