@article{article_1626396, title={Geometry of Harmonic Identity Maps}, journal={International Electronic Journal of Geometry}, volume={18}, pages={396–402}, year={2025}, DOI={10.36890/iejg.1626396}, author={Benkartab, Aicha and Mohammed Cherif, Ahmed}, keywords={Riemannian geometry, identity map, harmonic map}, abstract={An identity map $(M,g)\longrightarrow(M,g)$ is a harmonic from a Riemannian manifold $(M,g)$ onto itself. In this paper, we study the harmonicity of identity maps $(M,g)\longrightarrow(M,g-df\otimes df)$ and $(M,g-df\otimes df)\longrightarrow(M,g)$ where $f$ is a smooth function with gradient norm $<1$ on $(M,g)$. We construct new examples of identity harmonic maps. We define a symmetric tensor field on $M$ whose properties are related to the harmonicity of these identity maps.}, number={2}, publisher={Kazım İlarslan}