Exponentially Harmonic Maps, Gauss Maps and Gauss Sections

Abstract

We investigate the relationship of Ricci form, exponential tension field and tension field of the Gauss map of an immersion from a Riemannian manifold into a Riemannian space form. We also study exponentially harmonic Gauss sections which are the critical points of the vertical exponential energy through arbitrary vertical variations. We calculate the first variation of vertical exponential energy functional and discuss some related material.