6533b86cfe1ef96bd12c830f
RESEARCH PRODUCT
Minimal unit vector fields
Olga Gil-medranoElisa Llinares-fustersubject
Curl (mathematics)Killing vector fieldsSolenoidal vector fieldVector operatorcritical pointsGeneral Mathematicsminimal vector fieldsMathematical analysis53C4253C20Hopf vector fields53C25Sasakian manifoldsKilling vector fieldUnit vectorFundamental vector fieldMathematics::Differential GeometryVolume of vector fieldsComplex lamellar vector fieldVector potentialMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-03-01 | Tohoku Mathematical Journal |