本文主要利用一个自然恒等式并且考虑一类特殊(α,β)-流形 $\"\"$ 且φ(0)=1，其中？是Riemann度量， $\"\"$ 是一个1-形式。旨在利用自然恒等式研究一类特殊(α,β)-流形在一定条件下不存在闭的可定向的BH-极小子流形和闭的可定向的HT-极小曲面。
In this paper, we mainly use a natural identity and consider a class of special manifolds $\"\"$ with an (α,β)-metric $\"\"$ in which ？is the Riemannian metric, and $\"\"$ is a one-form. We aim to study a class of special manifolds by using the natural identity. Under certain conditions, there are no closed orientable BH-minimal submanifolds and closed orientable HT-minimal surfaces.