论文标题
liouville type定理（f; f'）p-harmonic在叶子上
Liouville type theorem for (F;F')p-harmonic maps on foliations
论文作者
论文摘要
在本文中，我们研究$（\ Mathcal f，\ Mathcal f'）_ {p} $ - 叶中的riemannian歧管$（m，g，\ m raimancal f）$和$（m'，g'，g'，\ mathcal f'）$之间的谐波图。 a $（\ MATHCAL F，\ MATHCAL F'）_ {p} $ - 谐波映射$ ϕ ：（ m，g，g，\ mathcal f）\ to（m'，g'，g'，\ mathcal f'）$是横向$ p $ p $ p $ - 增强功能的函数$ e_ e_ {b，p，p，p，p} $的关键点。琐事，$（\ MATHCAL F，\ MATHCAL F'）_ 2 $ -HARMONIC地图为$（\ Mathcal f，\ Mathcal f'）$ - 谐波映射，这是$ e_b $的关键点。在Foliated Riemannian歧管上，谐波图的另一个定义称为横向谐波映射，这是Euler-largrange方程$τ_b（ϕ）= 0 $的解决方案。两个定义不是等效的，但是如果$ \ MATHCAL F $很少，则两个定义是等效的。首先，我们为$（\ Mathcal f，\ Mathcal f'）_ {p} $ - 谐波映射提供了第一个和第二个变量公式。接下来，我们研究了广义的weitzenböck类型公式和liouville type定理，以$（\ mathcal f，\ mathcal f'）_ {p} $ - 谐波映射。
In this paper, we study $(\mathcal F,\mathcal F')_{p}$-harmonic maps between foliated Riemannian manifolds $(M,g,\mathcal F)$ and $(M',g',\mathcal F')$. A $(\mathcal F,\mathcal F')_{p}$-harmonic map $ϕ:(M,g,\mathcal F)\to (M', g',\mathcal F')$ is a critical point of the transversal $p$-energy functional $E_{B,p}$. Trivially, $(\mathcal F,\mathcal F')_2$-harmonic map is $(\mathcal F,\mathcal F')$-harmonic map, which is a critical point of $E_B$. There is another definition of a harmonic map on foliated Riemannian manifolds, called transversally harmonic map, which is a solution of the Euler-Largrange equation $τ_b(ϕ)=0$. Two definitions are not equivalent, but if $\mathcal F$ is minimal, then two definitons are equivalent. Firstly, we give the first and second variational formulas for $(\mathcal F,\mathcal F')_{p}$-harmonic maps. Next, we investigate the generalized Weitzenböck type formula and the Liouville type theorem for $(\mathcal F,\mathcal F')_{p}$-harmonic map.
