We consider harmonic maps $u(z):{\mathcal{X}}_z\to N$ in a fixed homotopy class from Riemann surfaces ${\mathcal{X}}_z$ of genus $g\ge 2$ varying in the Teichmüller space $\mathcal{T}$ to a Riemannian manifold N with non-positive Hermitian sectional curvature. The energy function $E(z)=E(u(z))$ can be viewed as a function on $\mathcal{T}$ and we study its first and the second variations. We prove that the reciprocal energy function $E{(z)}^{-1}$ is plurisuperharmonic on Teichmüller space. We also obtain the (strict) plurisubharmonicity of $\log E(z)$ and $E(z)$. As an application, we get the following relationship between the second variation of logarithmic energy function and the Weil-Petersson metric if the harmonic map $u(z)$ is holomorphic or anti-holomorphic and totally geodesic, i.e.,(0.1)$\sqrt{-1}\partial \overline{\partial }\log E(z)=\frac{{\omega }_{WP}}{2\pi (g-1)}.$ We consider also the energy function $E(z)$ associated to the harmonic maps from a fixed compact Kähler manifold M to Riemann surfaces ${\{{\mathcal{X}}_z\}}_{z\in \mathcal{T}}$ in a fixed homotopy class. If $u(z)$ is holomorphic or anti-holomorphic, then (0.1) is also proved.

我们考虑谐波图 $ü（ž）：{\mathcal{X}}_{ž}\to ñ$ 来自黎曼曲面的固定同伦类 ${\mathcal{X}}_{ž}$ 属 $G\ge 2$ 在Teichmüller空间中变化 $\mathcal{Ť}$到具有非正Hermitian截面曲率的黎曼流形N。能量功能$Ë（ž）=Ë（ü（ž））$ 可以看作是一个功能 $\mathcal{Ť}$我们研究了它的第一个和第二个变化。我们证明了倒数能量函数$Ë{（ž）}^{-\mathrm{1个}}$在Teichmüller空间上是超谐波的。我们还获得了（严格）的次谐波$\mathrm{日志}Ë（ž）$ 和 $Ë（ž）$。作为应用，如果调和图得到对数能量函数的第二个变化与Weil-Petersson度量之间的以下关系$ü（ž）$是全纯或反全纯的，并且完全测地线，即（0.1）$\sqrt{-\mathrm{1个}}\partial \overline{\partial }\mathrm{日志}Ë（ž）=\frac{{\omega }_{\mathrm{w\; ^}P}}{2\pi （G-\mathrm{1个}）}。$ 我们也考虑能量函数 $Ë（ž）$与从固定紧致的Kähler流形M到Riemann曲面的谐波映射相关联${\{{\mathcal{X}}_{ž}\}}_{ž\in \mathcal{Ť}}$在固定的同伦类中。如果$ü（ž）$ 是全纯或反全纯的，则还证明了（0.1）。