In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has no...In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.Such connections have already been classified in the work of Cartan(1924).The maps under consideration do not arise as critical points of an energy functional leading to interesting mathematical challenges.We will perform a first mathematical analysis of these maps which we will call harmonic maps with torsion.展开更多
基金support of the Austrian Science Fund(FWF)through the project P30749-N35“Geometric Variational Problems from String Theory”Open access funding provided by Austrian Science Fund(FWF)。
文摘In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.Such connections have already been classified in the work of Cartan(1924).The maps under consideration do not arise as critical points of an energy functional leading to interesting mathematical challenges.We will perform a first mathematical analysis of these maps which we will call harmonic maps with torsion.
