HS-tensional maps and HM-tensional maps

2025/09/10 by Bouazza Kacımı, Kacimi, Bouazza, Ahmed Mohammed Cherif +3
Mathematics · Physics and Astronomy · #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.2509.08564

openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ψ: (M,g)\longrightarrow (N,h) be a smooth map between Riemannian manifolds. The tension field of ψ can be regarded as a map from (M,g) into the Riemannian vector bundle ψ^-1TN, equipped with the Sasaki metric G_S. In this paper, we study certain aspects of two types of maps: those whose tension fields are harmonic maps (called HM-tensional maps) and those whose tension fields are harmonic sections (called HS-tensional maps).

Citations

• Biharmonic submanifolds of pseudo-Riemannian manifolds
• Biharmonic maps from a complete Riemannian manifold into a non-positively curved manifold
• Biharmonic properly immersed submanifolds in Euclidean spaces
• Classification results for biharmonic submanifolds in spheres
• Harmonic Mappings of Riemannian Manifolds

Related

• Harmonic maps and para-Sasakian geometry
• Maps with prescribed tension fields
• Harmonicity of sections of sphere bundles
• Removable singularities and bubbling of harmonic maps and biharmonic maps
• Harmonic sections of tangent bundles equipped with Riemannian g-natural metrics