Algebraic Harmonic Maps, Totally Symmetric Harmonic Maps and a Conjecture

Abstract

In this paper, we discuss the associated family of harmonic maps $\mathcal{F}:M\to G/K$ from a Riemann surface $M$ into inner symmetric spaces of compact or non-compact type which are either algebraic or totally symmetric. These notions are the two components of the definition of a harmonic map of finite uniton number, as stated by [2]. We finish this paper by comparing these to notions and by stating a conjecture.

23 pages. Partial content of the paper comes from the first part of arXiv:1305.2514v2