Biwarped product submanifolds of complex space forms
Biwarped product submanifolds of complex space forms
复制标题
复杂空间形式的双扭曲积子流形
DOI：
10.1142/s0219887819500725
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发表时间：
2019
影响因子：
1.8
通讯作者：
Kamran Khan
中科院分区：
文献类型：
--
作者：
M. Khan;Kamran Khan
双曲乘积流形是一类广义的乘积流形，是乘积流形的一个特例。本文研究了嵌入在复空间形式中的双曲积子流形[公式：见文本]。给出了这类子流形存在的几个特征不等式。此外，我们还利用翘曲函数和倾斜函数估计了第二基本形式的平方范数。这个不等式推广了Chen在[B.Y.Chen，在Kaehler流形I，Monatsh中的翘积CR子流形的几何]中得到的结果。数学课。133(2001)177-195]。利用导出的不等式，我们计算了所涉及的翘曲函数的Dirichlet能量。给出了这些翘曲积子流形的一个不平凡的例子。
The class of biwarped product manifolds is a generalized class of product manifolds and a special case of multiply warped product manifolds. In this paper, biwarped product submanifolds of the type [Formula: see text] embedded in the complex space forms are studied. Some characterizing inequalities for the existence of such type of submanifolds are derived. Moreover, we also estimate the squared norm of the second fundamental form in terms of the warping function and the slant function. This inequality generalizes the result obtained by Chen in [B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds I, Monatsh. Math. 133 (2001) 177–195]. By the application of derived inequality, we compute the Dirichlet energies of the warping functions involved. A nontrivial example of these warped product submanifolds is provided.