A conservation law for harmonic maps

1981 ◽  
pp. 1-25 ◽  
Author(s):  
P. Baird ◽  
J. Eells
Keyword(s):  
Conservation Law ◽  
Harmonic Maps

TRANSVERSALLY BIHARMONIC MAPS BETWEEN FOLIATED RIEMANNIAN MANIFOLDS

2008 ◽  
Vol 19 (08) ◽  
pp. 981-996 ◽  
Author(s):  
YUAN-JEN CHIANG ◽  
ROBERT A. WOLAK
Keyword(s):  
Riemannian Manifolds ◽  
Positive Constant ◽  
Conservation Law ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Biharmonic Maps ◽  
Foliated Manifold ◽  
Transverse Curvature ◽  
Biharmonic Map ◽  
Foliated Manifolds

We generalize the notions of transversally harmonic maps between foliated Riemannian manifolds into transversally biharmonic maps. We show that a transversally biharmonic map into a foliated manifold of non-positive transverse curvature is transversally harmonic. Then we construct examples of transversally biharmonic non-harmonic maps into foliated manifolds of positive transverse curvature. We also prove that if f is a stable transversally biharmonic map into a foliated manifold of positive constant transverse sectional curvature and f satisfies the transverse conservation law, then f is a transversally harmonic map.

A CONSERVATION LAW FOR HARMONIC MAPS

Harmonic Maps ◽  
1992 ◽  
pp. 131-155
Author(s):  
P. Baird ◽  
J. Eells
Keyword(s):  
Conservation Law ◽  
Harmonic Maps

A solution of the conservation law form of the Serre equations

2016 ◽  
Vol 57 ◽  
pp. 385
Author(s):  
Christopher Zoppou ◽  
Stephen Roberts ◽  
Jason Pitt
Keyword(s):  
Conservation Law

scholarly journals The zilch electromagnetic conservation law revisited

2020 ◽  
Vol 61 (12) ◽  
pp. 122902
Author(s):  
Sajad Aghapour ◽  
Lars Andersson ◽  
Kjell Rosquist
Keyword(s):  
Conservation Law

scholarly journals The magnetic helicity density patterns from non-axisymmetric solar dynamo

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Valery V. Pipin
Keyword(s):  
Magnetic Field ◽  
Differential Rotation ◽  
Conservation Law ◽  
Large Scale ◽  
Solar Dynamo ◽  
Magnetic Helicity ◽  
Dynamo Model ◽  
Density Distributions ◽  
Large Scale Magnetic Field ◽  
Helicity Conservation

We study the helicity density patterns which can result from the emerging bipolar regions. Using the relevant dynamo model and the magnetic helicity conservation law we find that the helicity density patterns around the bipolar regions depend on the configuration of the ambient large-scale magnetic field, and in general they show a quadrupole distribution. The position of this pattern relative to the equator can depend on the tilt of the bipolar region. We compute the time–latitude diagrams of the helicity density evolution. The longitudinally averaged effect of the bipolar regions shows two bands of sign for the density distributions in each hemisphere. Similar helicity density patterns are provided by the helicity density flux from the emerging bipolar regions subjected to surface differential rotation.

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