$HS$-tensional maps and $HM$-tensional maps

Abstract

Let $\psi :(M,g)⟶(N,h)$ be a smooth map between Riemannian manifolds. The tension field of $\psi$ can be regarded as a map from $(M,g)$ into the Riemannian vector bundle ${\psi }^{-1}TN$, equipped with the Sasaki metric $G_S$. In this paper, we study certain aspects of two types of maps: those whose tension fields are harmonic maps (called $HM$-tensional maps) and those whose tension fields are harmonic sections (called $HS$-tensional maps).