Harmonic maps from super Riemann surfaces

In this paper we study harmonic maps from super Riemann surfaces in complex projective spaces and projective spaces associated with the super skew-field D. In both cases, we develop the theory of Gauss transforms and study the notion of isotropy, in particular its relation to holomorphic differentials on the super Riemann surface. Moreover, we give a definition of finite type harmonic maps for a special class of maps into CPn vertical bar n+1 and thus obtain a classification for certain harmonic super tori. Furthermore, we investigate the equations satisfied by the underlying objects and give an example of a harmonic super torus in DP2 whose underlying map is not harmonic. (C) 2017 Elsevier B.V. All rights reserved.