Unit vector fields on antipodally punctured spheres: big index, big volume
Bulletin de la Société Mathématique de France, Volume 136 (2008) no. 1, pp. 147-157.

We establish in this paper a lower bound for the volume of a unit vector field v defined on 𝐒 n {±x}, n=2,3. This lower bound is related to the sum of the absolute values of the indices of v at x and -x.

Nous établissons une borne inférieure pour le volume d’un champ de vecteurs v défini dans 𝐒 n {±x}, n=2,3. Cette borne inférieure dépend de la somme des valeurs absolues des indices de v en x et en -x.

DOI: 10.24033/bsmf.2551
Classification: 53C20, 57R25, 53C12
Keywords: unit vector fields, volume, singularities, index
Mot clés : champs vectoriels unitaires, volume, singularités, indice
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Brito, Fabiano G. B.; Chacón, Pablo M.; Johnson, David L. Unit vector fields on antipodally punctured spheres: big index, big volume. Bulletin de la Société Mathématique de France, Volume 136 (2008) no. 1, pp. 147-157. doi : 10.24033/bsmf.2551. http://www.numdam.org/articles/10.24033/bsmf.2551/

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