Unit vector fields on antipodally punctured spheres: big index, big volume
Bulletin de la Société Mathématique de France, Volume 136 (2008) no. 1, p. 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 : https://doi.org/10.24033/bsmf.2551
Classification:  53C20,  57R25,  53C12
Keywords: unit vector fields, volume, singularities, index
@article{BSMF_2008__136_1_147_0,
     author = {Brito, Fabiano G. B. and Chac\'on, Pablo M. and Johnson, David L.},
     title = {Unit vector fields on antipodally punctured spheres: big index, big volume},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {136},
     number = {1},
     year = {2008},
     pages = {147-157},
     doi = {10.24033/bsmf.2551},
     zbl = {1158.53023},
     mrnumber = {2415338},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2008__136_1_147_0}
}
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/item/BSMF_2008__136_1_147_0/

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