论文标题
球形之间的双旋统均匀多项式图
Biharmonic homogeneous polynomial maps between spheres
论文作者
论文摘要
在本文中，我们首先证明了euclidean Spheres Biharmonic映射的特征性公式，并且作为一种应用，我们从一个平坦的$ 2 $ -Dimensional torus $ \ Mathbb {t} $中构建了一个Biharmonic Map家族，以$ 3 $ 3 $ 3 $ dimensional eucmensional euclidean spheys euclidean sphere $ \ mathbb $ \ mathbb {然后，对于由相同程度的均质多项式给出的球之间的特殊情况，我们为其替补场找到了更具体的形式。此外，我们将此公式应用于度为$ 2 $的情况下，并从$ \ Mathbb {s}^1 $到$ \ Mathbb {s}^n $，$ n \ geq 2 $中从$ \ mathbb {s}^1 $到$ \ geq 2 $，从$ \ mathbb { $ \ mathbb {s}^m $ to $ \ mathbb {s}^3 $，$ m \ geq 2 $。
In this paper we first prove a characterization formula for biharmonic maps in Euclidean spheres and, as an application, we construct a family of biharmonic maps from a flat $2$-dimensional torus $\mathbb{T}$ into the $3$-dimensional unit Euclidean sphere $\mathbb{S}^3$. Then, for the special case of maps between spheres whose components are given by homogeneous polynomials of the same degree, we find a more specific form for their bitension field. Further, we apply this formula to the case when the degree is $2$, and we obtain the classification of all proper biharmonic quadratic forms from $\mathbb{S}^1$ to $\mathbb{S}^n$, $n \geq 2$, from $\mathbb{S}^m$ to $\mathbb{S}^2$, $m \geq 2$, and from $\mathbb{S}^m$ to $\mathbb{S}^3$, $m \geq 2$.
