论文标题
Umehara代数和不确定复杂空间形式的复杂亚曼叶
Umehara algebra and complex submanifolds of indefinite complex space forms
论文作者
论文摘要
对乌梅哈拉代数的研究是在共同复杂子曼群不存在的问题上进行的。在本文中，我们证明了Umehara代数的一些新结果并获得了一些应用。特别是，如果一个复杂的歧管接收到一个不确定的复合空间形式的全体形态多项式均匀浸入，那么它就无法接收全体形态的等法浸入到不同类型的另一种不确定的复杂空间形式中。其他后果包括对于不确定的复杂射击空间或双曲空间的共同复杂亚符号的不存在，以及具有杰出的度量的复杂歧管，例如同质域，hartogs三角形，最小球，对称性的polydisc等，具有本质上的bergman，或者更少，或者更少地存在。
The Umehara algebra is studied with motivation on the problem of the non-existence of common complex submanifolds. In this paper, we prove some new results in Umehara algebra and obtain some applications. In particular, if a complex manifolds admits a holomorphic polynomial isometric immersion to one indefinite complex space form, then it cannot admits a holomorphic isometric immersion to another indefinite complex space form of different type. Other consequences include the non-existence of the common complex submanifolds for indefinite complex projective space or hyperbolic space and a complex manifold with a distinguished metric, such as homogeneous domains, the Hartogs triangle, the minimal ball, the symmetrized polydisc, etc, equipped with their intrinsic Bergman metrics, which generalizes more or less all existing results.
