arXiv Open Access 2025

Geometry of Harmonic Identity Maps

Aicha Benkartab Ahmed Mohammed Cherif

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Abstrak

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.

Topik & Kata Kunci

math.DG

Penulis (2)

Aicha Benkartab

Ahmed Mohammed Cherif

Format Sitasi

APA MLA BibTeX

Benkartab, A., Cherif, A.M. (2025). Geometry of Harmonic Identity Maps. https://arxiv.org/abs/2501.01804

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓