论文标题
一般的不平等和新形状的操作员不平等，用于宇宙空间形式的CR-WARPED PRODUCT SUBMANIFOLDS
General inequalities and new shape operator inequality for contact CR-warped product submanifolds in cosymplectic space form
论文作者
论文摘要
我们建立了两个主要的不平等现象；一种用于第二个基本形式的规范，另一个用于形状操作员的矩阵。获得的结果是用于恢复歧管的，为此，我们表明触点扭曲的产物submanifolds自然具有几何特性。即$ \ MATHCAL {D} _1 $ - 最小程度，通过高斯方程式，我们可以获得最佳的一般不等式。为了进行概括，我们说明了几乎偶然歧管的假设，然后将它们作为偶然歧管的特殊案例。对于本文的另一部分，我们得出了一些不平等现象，并将其应用于构建和引入形状操作员的不平等，以涉及涉及谐波系列的cosimpledic歧管。作为进一步的研究方向，我们在这项工作中自然而然地解决了一些开放问题，这取决于其结果。
We establish two main inequalities; one for the norm of the second fundamental form and the other for the matrix of the shape operator. The results obtained are for cosymplectic manifolds and, for these, we show that the contact warped product submanifolds naturally possess a geometric property; namely $\mathcal{D}_1$-minimality which, by means of the Gauss equation, allows us to obtain an optimal general inequality. For sake of generalization, we state our hypotheses for nearly cosymplectic manifolds, then we obtain them as particular cases for cosymplectic manifolds. For the other part of the paper, we derived some inequalities and applied them to construct and introduce a shape operator inequality for cosimpleptic manifolds involving the harmonic series. As further research directions, we have addressed a couple of open problems arose naturally during this work and which depend on its results.
