Harmonic maps on Sasakian manifolds

Abstract

The theory of harmonic maps on Riemannian and Kahlerian manifolds is very rich in interesting results and continues to be one of the most important areas of differential geometry. A map between Riemannian manifolds is called harmonic if the divergence of its differential vanishes. For Riemannian manifolds with a differential structure, it is known that a smooth holomorphic map between Kaehler manifolds is harmonic. The study of harmonic maps on contact metric manifolds was initiated by Ianus et. al.. In this paper we consider harmonic maps on Sasakian manifolds and also discuss the non-existence of such maps.