Year: 2025
Type: article
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.
Authors: Aicha Benkartab, Ahmed Mohammed Cherif
Institution: Université Mustapha Stambouli de Mascara
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4415115087