论文标题
关于矢量场的插值squi谐波
On the Interpolating Sesqui-Harmonicity of Vector Fields
论文作者
论文摘要
本文介绍了矢量字段的插值seSqui-harmonicity $ x $被视为来自Riemannian歧管$（m，g）$的地图，以与Sasaki Metric $ g_ {s} $赋予其切线捆绑包$ tm $。我们显示了$ x $的表征定理，用于插值sesqui-harmonic地图。我们还提供了特征在于插值seSqui-harmonic矢量场的临界点条件。当$（m，g）$紧凑且定向时，在某些条件下，我们证明$ x $是一个插值sesqui-harmonic矢量场（分别插值sesqui-harmonic Map），并且仅当$ x $是平行的时。此外，我们将此结果扩展到具有离散亚组$γ$的Lie组$ G $上的左行矢量场，以使商$γ\ Backslash G $紧凑。
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.
