Holomorphic maps into Grassmann manifolds (Harmonic maps into Grassmann manifolds III),
Holomorphic maps into Grassmann manifolds (Harmonic maps into Grassmann manifolds III),
复制标题
全纯映射到格拉斯曼流形（调和映射到格拉斯曼流形 III），
DOI：
10.1007/s10455-021-09765-6
复制
发表时间：
2021
影响因子：
0.7
通讯作者：
Yasuyuki Nagatomo
中科院分区：
文献类型：
--
作者：
Kawai Kotaro;Yamamoto Hikaru;Yasuyuki Nagatomo;宇田川誠一;河井 公大朗;Seiichi Udagawa;Koga Isami and Nagatomo Yasuyuki;宇田川 誠一;Kotaro Kawai;Yasuyuki Nagatomo
将复射影空间中关于全纯等距浸入的著名Calabi刚性定理推广到复Grassmann流形的情形。我们的策略是使用微分几何的向量丛和推广做Carmo和Wallach理论开发的Nagatomo（调和映射到格拉斯曼流形。 arXiv：mathDG/1408.1504 ).我们引进了全纯映射的伴随映射，得到了一个一般的刚性定理（定理5.6）。作为应用，给出了Einstein-Hermitian全纯映射的几个刚性结果，并给出了紧Kähler流形到复二次曲面的全纯等距嵌入的模空间上存在一个带作用的Kähler结构的解释.定理5.6也包含了等变全纯映射的分类定理。
A well-known Calabi’s rigidity theorem on holomorphic isometric immersions into the complex projective space is generalized to the case that the target is the complex Grassmann manifolds. Our strategy is to use the differential geometry of vector bundles and a generalization of do Carmo and Wallach theory developed in Nagatomo (Harmonic maps into Grassmann manifolds. arXiv:mathDG/1408.1504 ). We introduce the associated maps with holomorphic maps to obtain a general rigidity theorem (Theorem 5.6). As applications, several rigidity results on Einstein–Hermitian holomorphic maps are exhibited and we also give an interpretation of the existence of a Kähler structure with an-action on the moduli spaces of holomorphic isometric embeddings of a compact Kähler manifold into complex quadrics. Theorem 5.6 also implies classification theorems for equivariant holomorphic maps.