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数学进展 - 2016, Vol. 45(2): 271-289
研究论文
近凯勒流形中一般子流形的淹没
Submersions of Generic Submanifolds a Nearly Kä|hler Manifold

朱晴晴,杨标桂
ZHU Qingqing, YANG Biaogui

福建师范大学数学与计算机科学学院, 福州, 福建, 350117
School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian, 350117, P. R. China

收稿日期: 2014-08-27
出版日期: 2016-03-10
2016, Vol. 45(2): 271-289
DOI: 10.11845/sxjz.2014129b


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摘要 本文讨论了近凯勒(nearly Kähler)流形中一般子流形的淹没, 证明了: 如果$\pi:M\rightarrow B$是近凯勒流形$\bar{M中子流形$M$到殆埃尔米特(almost Hermitian)流形$B$的淹没, 那么$B$是近凯勒流形. 另外, 本文给出了关于这种淹没分解理论的一些性质, 并且研究了$\bar{M和$B$的全纯截面曲率之间的关系.
Abstract:In this paper, we discuss submersions of generic submanifolds of a nearly Kä|hler manifold. We prove that if $\pi:M\rightarrow B$ is a submersion of generic submanifold $M$ of a nearly Kä|hler manifold $\bar{M onto an almost Hermitian manifold $B$, then $B$ is a nearly Kä|hler manifold. We also obtain the decomposition theorems for such submersions and derive the relation between the holomorphic sectional curvatures of $\bar{M and that of $B$.
PACS:  O186.12  
基金资助:国家自然科学基金(No. 11171139, No. 11401099), 福建省自然科学基金(No. 2011J05001)和福建省教育厅A类项目(No. JA11052).
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