Energy and topology of singular unit vector fields on S³ 27

• Autores: Pablo M. Chacón, Giovanni da Silva Nunes
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 231, Nº 1, 2007, págs. 27-34
• Idioma: inglés
• DOI: 10.2140/pjm.2007.231.27
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• Resumen

  • The energy of unit vector fields on odd-dimensional spheres is a functional that has a minimum in dimension 3 and an infimum in higher dimensions. Vector fields with isolated singularities arise naturally in the study of this functional. We consider the class of fields in S3 having two antipodal singularities. We prove a lower bound, attained for the radial vector field, for the energy of this class of fields in terms of the indices of the singularities. A similar inequality is not to be expected in other dimensions.