TY  - JOUR
T1  - Geometry of Harmonic Identity Maps
AU  - Mohammed Cherif, Ahmed
AU  - Benkartab, Aicha
PY  - 2025
DA  - October
Y2  - 2025
DO  - 10.36890/iejg.1626396
JF  - International Electronic Journal of Geometry
JO  - Int. Electron. J. Geom.
PB  - Kazım İlarslan
WT  - DergiPark
SN  - 1307-5624
SP  - 396
EP  - 402
VL  - 18
IS  - 2
LA  - en
AB  - 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.
KW  - Riemannian geometry
KW  - identity map
KW  - harmonic map
CR  - Baird, P. and Wood,J. C. :Harmonic morphisms between Riemannain manifolds. Clarendon Press, Oxford (2003).
CR  - Benkartab, A. and Mohammed Cherif, A.: New methods of construction for biharmonic maps, Kyungpook Math. J. 59(2019), 135–147.
CR  - Benkartab, A. and Mohammed Cherif, A.: Deformations of Metrics and Biharmonic Maps, Commun. Math. 28 (2020), 263–275.
CR  - Eells, J.and Lemaire, L.:A report on harmonic maps. Bull. London Math. Soc. 16, 1–68(1978).
CR  - Eells, J.and Lemaire,L.: Another report on harmonic maps. Bull. London Math. Soc. 20 , 385–524(1988).
CR  - Eells, J. and Sampson,J. H.: Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86, 109–160(1964).
CR  - Merdji, B. and Mohammed Cherif, A.: New types of metrics deformations and applications to p-biharmonic maps. J. Indian Math. Soc. 90
(3-4) , 387–400(2023).
CR  - Udrişte, C.: Convex Functions and Optimization Methods on Riemannian Manifolds. Mathematics and Its Applications, Kluwer
Academic Publishers: Dordrecht, The Netherlands, 1994.
CR  - Sakai, T.: Riemannian Geometry. Shokabo, Tokyo (1992). (in Japanese).
CR  - Topping, P. : Lectures on the Ricci Flow. Number 325 in London Mathematical Society Lecture Note Series. Cambridge University Press,
October, 2006.
UR  - https://doi.org/10.36890/iejg.1626396
L1  - https://dergipark.org.tr/en/download/article-file/4549774
ER  -