The constant osculating rank of the Wilking manifold $ {V}_{3}$

Macías-Virgós, Enrique; Naveira, Antonio M.; Tarrío, Ana

doi:10.1016/j.crma.2007.11.009

Differential Geometry

The constant osculating rank of the Wilking manifold

V_{3}

[Le rang osculateur constant de la variété de Wilking

V_{3}

]

Présenté par : Thierry Aubin

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

Comptes Rendus. Mathématique, Tome 346 (2008) no. 1-2, pp. 67-70.

Résumé
Abstract

Nous prouvons que le rang osculateur de la variété de Wilking $V_{3} = (SO (3) \times SU (3)) / U^{•} (2)$ vaut 2, lorsque on considère la metrique ${\tilde{g}}_{1}$ . 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.

We prove that the osculating rank of the Wilking manifold $V_{3} = (SO (3) \times SU (3)) / U^{•} (2)$ , endowed with the metric ${\tilde{g}}_{1}$ , 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.

Reçu le : 2007-09-04
Accepté le : 2007-11-08
Publié le : 2008-01-01

DOI : 10.1016/j.crma.2007.11.009

Affiliations des auteurs :

Macías-Virgós, Enrique ¹ ; Naveira, Antonio M. ² ; Tarrío, Ana ³

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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, Tome 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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Cité par Sources :

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