UNIT VECTOR FIELDS ON ANTIPODALLY PUNCTURED SPHERES: BIG INDEX, BIG VOLUME

We establish in this paper a lower bound for the volume of a unit vector field (v) over right arrow defined ou S(n) \ {+/-x}, n = 2,3. This lower bound is related to the sum of the absolute values of the indices of (v) over right arrow at x and -x.

MEC/FEDER, Spain[MTM2004-04934-C04-02]

MEC-FEDER, Spain

Universidade de Sao Paulo (USP), FAPESP[1999/02684-5]

Universidade de Sao Paulo (USP)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Lehigh University

Lehigh University