SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN'S INEQUALITY  

作　　者：李光汉 吴传喜 

机构地区：[1]School of Mathematical Science Peking University, Beijing 100871,China,School of Mathematics and Computer Science,Hubei University,Wuhan 430062,China,School of Mathematics and Computer Science Hubei University,Wuhan 430062,China

出　　处：《Acta Mathematica Scientia》2005年第2期223-232,共10页数学物理学报（B辑英文版）

基　　金：This project is supported by the NSFC(10271041)Tianyuan Youth Foundation of Mathematics.

摘　　要：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.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.

关 键 词：Slant immersion IDEAL Chen's inequality complex space form 

分 类 号：O178[理学—数学]