On Characterizations of Hopf Hypersurfaces in a Nonflat Complex Space Form with Anti-commuting Operators

详细信息    查看全文

• 作者：In-Bae Kim ; Dong Ho Lim ; Woon Ha Sohn
• 关键词：Real hypersurface ; structure Jacobi operator ; Hopf hypersurface ; model spaces
• 刊名：Results in Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：71
• 期：1-2
• 页码：197-210
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1420-9012
• 卷排序：71

文摘

Let M be a real hypersurface in a complex space form M_n(c), \({c \neq 0}\). In this paper we prove that if \({R_{\xi}(\phi A - A\phi) + (\phi A - A\phi)R_{\xi} = 0}\) holds on M, then M is a Hopf hypersurface, where \({R_{\xi}}\) is the structure Jacobi operator, A is the shape operator of M in M_n(c) and \({\phi}\) is the tangential projection of the complex structure of M_n(c). We characterize such Hopf hypersurfaces of M_n(c).