| SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN＇S INEQUALITY |
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| 引用本文： | 李光汉,吴传喜.SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN＇S INEQUALITY[J].数学物理学报(B辑英文版),2005,25(2):223-232. |
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| 作者姓名： | 李光汉 吴传喜 |
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| 作者单位： | [1]SchoolofMathematicsandComputerScience,HubeiUniversity,Wuhan430062 [2]SchoolofMathematicalScience,PekingUniversity,Beijing100871,China／／SchoolofMathematicsandComputerScience,HubeiUniversity,Wuhan430062 |
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| 基金项目： | 国家自然科学基金，Tianyuan Youth Foundation of Mathematics |
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| 摘 要： | A submanifold in a complex space form is called slant it it has constant Wirtinger angles. B, Y, Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP^2 and CH^2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions satisfying some additional conditions, such as unfull first normal bundles or Chen‘s equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersion sin CP^n and CH^n with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen‘s inequality to general slant immersions in a complex projective space, which generalizes a result of Chen.
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| 关 键 词： | 理想 复空间形式 Chen’s不等式 子流形 斜浸入 |
| 收稿时间： | 10 December 2002 |
SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN'S INEQUALITY |
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| Li Guanghan,Wu Chuanxi.SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN''''S INEQUALITY[J].Acta Mathematica Scientia,2005,25(2):223-232. |
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| Authors: | Li Guanghan Wu Chuanxi |
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| Institution: | 2. School of Mathematical Science, Peking University, Beijing 100871, China;3. School of Mathematics and Computer Science, Hubei University, Wuhan 430062, China;1. Departamento de Geometría y Topología, c/ Tarfia s/n, Universidad de Sevilla, Sevilla 41012, Spain;2. Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), c/ Nicolás Cabrera no. 13-15, Campus de Cantoblanco, UAM, Madrid 28049, Spain;1. College of Science, Changʼan University, Xiʼan, Shaanxi, 710064, PR China;2. College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, PR China;1. Department of Mathematics, Mascara University, Algeria;2. L.G.A.C.A Laboratory of Saida University, Algeria;3. Department of Mathematics, Relizane University, Algeria;4. G.M.F.A.M.I Laboratory of Relizane University, Algeria |
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| Abstract: | A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions satisfying some additional conditions, such as unfull first normal bundles or Chen's equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersions in CPn and CHn with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen's inequality to general slant immersions in a complex projective space, which generalizes a result of Chen. |
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| Keywords: | Slant immersion ideal Chen's inequality complex space form |
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