On generalized Cheeger-Gromoll metric and harmonicity

Abstract

In this paper, we introduce the Generalized Cheeger-Gromoll metric on the tangent bundle TM, as a natural metric on TM. We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the Generalized Cheeger-Gromoll metric. We also construct some examples of harmonic vector fields.

Keywords

• Horizontal lift,vertical lift,generalized Cheeger-Gromoll metric,harmonic maps

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