Abstract
This chapter discusses fundamental matters such as the Dirichlet energy and tension tensor of a unit tangent vector field on a Riemannian manifold, first and second variation formulae, and the harmonic vector fields system. The study of the weak solutions to this system (existence and local properties) is missing from the present day mathematical literature. Various instances are investigated where harmonic vector fields occur and to generalizations. Any unit vector field that is a harmonic map is also a harmonic vector field. The study of harmonic map system is more appropriate on a Hermitian manifold and that results in Hermitian harmonic maps to be useful in studying rigidity of complete Hermitian manifolds.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call