Biharmonic homomorphisms between Riemannian Lie groups

2014/07/17 by Mohamed Boucetta, Boucetta, Mohamed, Seddik Ouakkas +1
Mathematics · Physics and Astronomy · #22E15 #53C30 #53C43 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1407.4853

openalex publication_date 2014/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Lie group G endowed with a left invariant Riemannian metric g is called Riemannian Lie group. Harmonic and biharmonic maps between Riemannian manifolds is an important area of investigation. In this paper, we study different aspects of harmonic and biharmonic homomorphisms between Riemannian Lie groups. We show that this class of biharmonic maps can be used at the first level to build examples but, as we will see through this paper, its study will lead to some interesting mathematical problems in the theory of Riemannian Lie groups.

Citations

• Harmonic Mappings of Riemannian Manifolds
• Curvatures of left invariant metrics on lie groups

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