The present paper aims to construct an inequality for bi-warped product submanifolds in a special class of almost metric manifolds, namely nearly Kenmotsu manifolds. As geometric applications, some exceptional cases that generalized several other inequalities are discussed. We also deliberate some applications in the context of mathematical physics and derive a new relation between the Dirichlet energy and the second fundamental form. Finally, we present a constructive remark at the end of this paper which shows the motive of the study.

中文翻译：

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几乎Kenmotsu流形的双向翘曲子流形的几何不等式及其应用

本文旨在构造一类特殊的近似度量流形，即近似Kenmotsu流形的双翘乘积子流形的不等式。作为几何应用，讨论了一些导致其他不等式普遍化的特殊情况。我们还讨论了数学物理学中的一些应用，并得出了狄利克雷能量与第二基本形式之间的新关系。最后，我们在本文结尾处提出了建设性的意见，表明了研究的动机。