Volumes of Vector Fields on Spheres
Open Access
- 1 March 1993
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 336 (1) , 69-78
- https://doi.org/10.2307/2154338
Abstract
In this paper we study the problem: What is the unit vector field of smallest volume on an odd-dimensional sphere? We exhibit on each sphere a unit vector field with singularity which has exceptionally small volume on spheres of dimension greater than four. We conjecture that this volume is the infimum for volumes of bona fide unit vector fields, and is only achieved by the singular vector field.Keywords
This publication has 3 references indexed in Scilit:
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- On the volume of a unit vector field on the three-sphereCommentarii Mathematici Helvetici, 1986
- Certain minimal or homologically volume minimizing submanifolds in compact symmetric spacesTsukuba Journal of Mathematics, 1985