调和叶状结构--一个有趣的公式(观点)

\[E(\mathcal{F})=\frac{1}{2}||\pi||^2= \frac{1}{2} \int _M g_Q(\pi\wedge * \pi) \]

Theorem: Let $\mathcal{F}$ be a foliation on a manifold $M$ and $g_M$ a Riemannian metric. Then all the leaves of the foliation are minimal submanifolds of $M$ if and only if the canonical $Q$ -valued 1-form $\pi : TM \to Q $ is harmonic.