论文标题
在Picard第一
Splitting submanifolds in rational homogeneous spaces of Picard number one
论文作者
论文摘要
令$ m $为复杂的歧管。我们证明，当$ m $位于PICARD第一的一大批合理同质空间中时，带有分裂切线序列（称为拆分submanifold）的紧凑型Submanifold $ S \子集M $是合理的。此外，当$ m $不可约遗传性对称时，我们证明$ s $也必须是赫尔米尼亚对称性。我们使用的基本工具是从拆分条件引起的环境空间上全局全态向量场的限制和投影图$π$。全局全体形态矢量场的使用可能有助于我们建立一个新方案，以明确的示例中的分裂子策略进行分类，例如，我们给出了与$ \ \ dim \ dim \ geq 2 $分类的差分几何证明，以先前使用Algebraic Geometry preved。
Let $M$ be a complex manifold. We prove that a compact submanifold $S\subset M$ with splitting tangent sequence (called a splitting submanifold) is rational homogeneous when $M$ is in a large class of rational homogeneous spaces of Picard number one. Moreover, when $M$ is irreducible Hermitian symmetric, we prove that $S$ must be also Hermitian symmetric. The basic tool we use is the restriction and projection map $π$ of the global holomorphic vector fields on the ambient space which is induced from the splitting condition. The usage of global holomorphic vector fields may help us set up a new scheme to classify the splitting submanifolds in explicit examples, as an example we give a differential geometric proof for the classification of compact splitting submanifolds with $\dim\geq 2$ in a hyperquadric, which has been previously proven using algebraic geometry.
