On the Interpolating Sesqui-Harmonicity of Vector Fields

2022/11/01 by Bouazza Kacımı, Kacimi, Bouazza, Amina Alem +3
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2211.00443

openalex publication_date 2022/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article deals with the interpolating sesqui-harmonicity of a vector field X viewed as a map from a Riemannian manifold (M,g) to its tangent bundle TM endowed with the Sasaki metric g_S. We show characterization theorem for X to be interpolating sesqui-harmonic map. We give also the critical point condition which characterizes interpolating sesqui-harmonic vector fields. When (M,g) is compact and oriented and under some conditions, we prove that X is an interpolating sesqui-harmonic vector field (resp. interpolating sesqui-harmonic map) if and only if X is parallel. Moreover, we extend this result for a left-invariant vector field on a Lie group G having a discrete subgroup Γ such that the quotient Γ\backslash G is compact.

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