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2002 Minimal unit vector fields
Olga Gil-Medrano, Elisa Llinares-Fuster
Tohoku Math. J. (2) 54(1): 71-84 (2002). DOI: 10.2748/tmj/1113247180

Abstract

We compute the first variation of the functional that assigns each unit vector field the volume of its image in the unit tangent bundle. It is shown that critical points are exactly those vector fields that determine a minimal immersion. We also find a necessary and sufficient condition that a vector field, defined in an open manifold, must fulfill to be minimal, and obtain a simpler equivalent condition when the vector field is Killing. The condition is fulfilled, in particular, by the characteristic vector field of a Sasakian manifold and by Hopf vector fields on spheres.

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Olga Gil-Medrano. Elisa Llinares-Fuster. "Minimal unit vector fields." Tohoku Math. J. (2) 54 (1) 71 - 84, 2002. https://doi.org/10.2748/tmj/1113247180

Information

Published: 2002
First available in Project Euclid: 11 April 2005

zbMATH: 1006.53053
MathSciNet: MR1878928
Digital Object Identifier: 10.2748/tmj/1113247180

Subjects:
Primary: 53C42
Secondary: 53C20, 53C25

Rights: Copyright © 2002 Tohoku University

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