In the present paper, we prove that there does not exist any \(\mathcal {P}\mathcal {R}\)-semi-slant warped product submanifolds in paracosymplectic manifolds. In addition, by presenting a non-trivial example we find that there is no proper \(\mathcal {P}\mathcal {R}\)-semi-slant warped product submanifold other than \(\mathcal {P}\mathcal {R}\)-semi-invariant warped products.

中文翻译：

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$$ \ mathcal {P} \ mathcal {R} $$ PR的不存在-旁缩歧管中的半倾斜翘曲积子流形

在本文中，我们证明在副凸形歧管中不存在任何\（\ mathcal {P} \ mathcal {R} \） -半倾斜翘曲积子流形。另外，通过呈现一个非平凡例子中，我们发现，没有适当的\（\ mathcal {P} \ mathcal {R} \） -半倾斜翘曲产品子流形比其他\（\ mathcal {P} \ {mathcal R} \） -半不变翘曲积。