论文标题
Berger空间的协会子曼菲尔德
Associative Submanifolds of the Berger Space
论文作者
论文摘要
我们研究Berger空间的关联亚策略SO（5）/SO（3）赋予其几乎平行的G2结构。我们专注于两个几何有趣的类：被统治的协会和具有特殊高斯地图的协会。 我们表明，由$ gr_2^+（ts^4）中的伪单晶曲线（ts^4）。$使用此通信以及Bryem在超级金色表面上的定理中，$ s^4中的超级层面上的$ s^4，我们在$ s^4中，我们在$ s^4中的生存中，我们在$ gr_2^+（ts^4）中均与伪单晶曲线相称。$ gr_2^+（TS^4）。因此（5）/so（3）。 据说，如果其切线空间具有非平凡的SO（3） - 稳定器，则据说Berger空间的协会子曼属具有特殊的高斯图。在稳定剂包含大于2的级数的情况下，我们将关联子手机构图与特殊高斯图分类。特别是，我们发现了这种类型的几个同质示例。
We study associative submanifolds of the Berger space SO(5)/SO(3) endowed with its homogeneous nearly-parallel G2-structure. We focus on two geometrically interesting classes: the ruled associatives, and the associatives with special Gauss map. We show that the associative submanifolds ruled by a certain special type of geodesic are in correspondence with pseudo-holomorphic curves in $Gr_2^+(TS^4).$ Using this correspondence, together with a theorem of Bryant on superminimal surfaces in $S^4,$ we prove the existence of infinitely many topological types of compact immersed associative 3-folds in SO(5)/SO(3). An associative submanifold of the Berger space is said to have special Gauss map if its tangent spaces have non-trivial SO(3)-stabiliser. We classify the associative submanifolds with special Gauss map in the cases where the stabiliser contains an element of order greater than 2. In particular, we find several homogeneous examples of this type.
