Harmonicity of deformed gradient metric

Abstract

Let (M^m_, g) be an m-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on (M^m, g) called the deformed gradient metric. First we investigate the Levi-Civita connection of this metric. Secondly we study some properties of harmonicity with respect to the deformed gradient metric. We also construct some examples of harmonic maps.