Differential Geometry
The constant osculating rank of the Wilking manifold V3
Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 67-70.

We prove that the osculating rank of the Wilking manifold V3=(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.

Nous prouvons que le rang osculateur de la variété de Wilking V3=(SO(3)×SU(3))/U(2) vaut 2, lorsque on considère la metrique g˜1. La connaissance du rang osculateur nous permet de resoudre l'équation différentielle des champs de vecteurs de Jacobi. Ces résultats peuvent être appliqués pour déterminer l'aire et le volume des sphères et boules géodesiques.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.11.009
Macías-Virgós, Enrique 1; Naveira, Antonio M. 2; Tarrío, Ana 3

1 Dpto. de Xeometría e Topoloxía, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
2 Dpto. de Geometría y Topología, Facultad de Matemáticas, Avda. A. Estellés, No 1. 46100 Burjassot, Valencia, Spain
3 E. U. Arquitectura Técnica, Universidade de A Coruña, Campus A Zapateira, 15192 A Coruña, Spain
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Macías-Virgós, Enrique; Naveira, Antonio M.; Tarrío, Ana. The constant osculating rank of the Wilking manifold $ {V}_{3}$. Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 67-70. doi : 10.1016/j.crma.2007.11.009. http://www.numdam.org/articles/10.1016/j.crma.2007.11.009/

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Work partially supported by Research Projects MTM2004-05082 (first author), MTM-2007-65852 (second author) and PGIDIT05PXIB16601PR (third author).